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https://math.stackexchange.com/questions/2641534/if-cos-theta-is-rational-then-is-cos-k-theta-also-rational
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# If $\cos\theta$ is rational, then is $\cos k\theta$ also rational?
If $\cos\theta$ is rational, then is $\cos k\theta$ also rational, where $k$ is a positive integer? I tried a few simple cases, and they worked. Is it true? And if it is then how do I go about rigorously proving this?
I've tried using the identity of $\cos(A+B)$ with induction, but am not able to prove it.
Thanks.
We have $$\cos k\theta=T_k(\cos\theta)$$ where $T_k$ is the $k$th Chebyshev polynomial of the first kind. Since all Chebyshev polynomials have integral coefficients and $\cos\theta$ is rational, $\cos k\theta$ must also be rational.
For a lower-level proof, de Moivre's formula gives $\cos k\theta$ as the real part of $(\cos\theta+i\sin\theta)^k$, expanding to $$\cos k\theta=\sum_{l=0}^{\lfloor k/2\rfloor}\binom k{2l}\sin^{2l}\theta\cos^{k-2l}\theta$$ Since $\sin^2x=1-\cos^2x$: $$\cos k\theta=\sum_{l=0}^{\lfloor k/2\rfloor}\binom k{2l}(1-\cos^2\theta)^l\cos^{k-2l}\theta$$ Since binomial coefficients are integers, the RHS is an integer polynomial in $\cos\theta$, so $\cos k\theta$ is rational. In fact, this polynomial is one way to define the $T_k$.
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2019-07-21 15:08:53
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https://www.jobilize.com/course/section/experiment-design-computational-experiment-of-ffast-by-openstax?qcr=www.quizover.com
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# 0.4 Computational experiment of ffast
Page 1 / 1
## Experiment design
We wanted to determine the most computationally efficient demodulation method for the digital multitone scheme. In our experiment, we compared the operation counts of an optimized FFT meta algorithm, a partial DFT computation (the DFT computed only for the nonzero coefficients), and FFAST in demodulating various message signals. We chose these demodulation methods because they are currently the most efficient methods for DMT demodulation. The experiments were run using MATLAB 2014a. We chose to run our experiment in MATLAB for its rapid prototyping environment.
While we were interested in comparing the computational efficiency of these algorithms, we chose to record operation counts rather than run times. Run times are unreliable metrics on machines with multitasking operating systems, especially when using highly optimized programs like MATLAB. We chose to count complex additions and multiplications as one operation each. We did not count conditional statements as operations because in most general processors, they only require a single cycle. We counted complex exponentials and trigonometric functions as one operation because they may be implemented using lookup tables.
## Meta-fft algorithm implementation
The two main goals for our implementation of the optimized FFT meta algorithm were to i) create an algorithm that performs without the need to zero-pad the signal and ii) allows us to count operations. Well-behaved signal lengths in our implementation of the algorithm have the form of $N={n}_{0}{n}_{1}{n}_{2}$ , where ${n}_{i}$ are coprimes. To exploit this structure, the optimized FFT meta algorithm, implemented in meta_fft.m , uses a self-sorting mixed-radix complex FFT [link] . For sub-transforms of length $2\le N\le 6$ , short-length Winograd transforms are applied to conserve operation count. All other transforms are computed using Rader's FFT algorithm [link] .
## Ffast implementation
The FFAST algorithm implementation requires the signal itself, the length of the signal, and a vector of the downsampling coefficients.
The FFAST algorithm was implemented in two files. The first file, ffast_front_end.m , downsamples the signal by each of the coprimes and feeds shifted and unshifted versions of the downsampling to the meta_fft.m file, to get operation counts and the relevant FFTs. Once the relevant DFT pairs are generated, ffast_front_end.m calls the back end of the algorithm.
The second file, peeling_decoder.m , implements the peeling module of FFAST to backsolve the bipartite graph. The program will return a flag if the algorithm encounters no singletons at a stage where it has not been fully solved.
## Numerical results
In our first experiment, we varied the signal length N and observed the operation counts required for the optimized FFT meta algorithm, the partial DFT, and FFAST. We constructed each signal in the Fourier domain by randomly selecting $k$ values from the set of integers $\left\{1,\cdots ,N\right\}$ and setting the corresponding DFT coefficients to $\frac{k}{2}$ . For each signal, we put $k={N}^{1/3}$ , which is the greatest allowed sparsity in our scheme. The choice of $k$ and values of the $k$ nonzero DFT coefficients are consistent with the DMT scheme. We used MATLAB's library function ifft() to compute the corresponding signal and counted the number of operations it took each algorithm to compute the DFT. We observed that the operation count required for FFAST was usually an order of magnitude less that the operation counts required for both the meta FFT algorithm and the partial DFT. See Fig [link] for the results of the first experiment.
In our second experiment, we varied the signal sparsity $k$ and observed the operation count required for the optimized FFT meta algorithm, the partial DFT, and FFAST. For this experiment, signal length $N=8740$ and the signals were constructed in the Fourier domain, as before. We observed an $80%$ computational decrease from the optimized FFT to FFAST for all $k<{N}^{\frac{1}{3}}$ . However, for $k>{N}^{\frac{1}{3}}$ , we observed signals for which FFAST did not converge. See Fig [link] for the results of the second experiment.
Note that the operation count for the partial DFT is less than the operation count for FFAST for $k<8$ ; this is somewhat misleading because the way that the partial DFT is computed is slightly optimistic. The partial DFT computes only the nonzero coefficients, which are known a priori in this experiment. In the general framework of DMT, one would need to compute all possibly nonzero DFT coefficients, resulting in an operation count higher than that of FFAST.
#### Questions & Answers
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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2019-04-21 02:07:40
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https://quant.stackexchange.com/questions/40852/why-is-the-expected-value-of-bias-statistic-one
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# Why is the expected value of bias statistic one?
I have been reading about factor models recently. One of the ways in which the developer of these models (Barra/ Axioma) measure the accuracy of their models is by calculating the bias statistic for the risk forecasts provided by these models.
Basically, the process to calculate bias statistic has four legs -
a. At each time period t, forecast the risk of the portfolio. Let this be $sigma_t$ b. Calculate the return of the portfolio over the forecasting horizon (from time t to t+1). Let this be $r_t$ c. Calculate the standardized returns of the portfolio, $Z_t = r_t / sigma_t$ d. Do this T number of times. Bias Statistic will be the standard deviation of the standardized returns $Z_t$
What I fail to understand here is why should the expected value of the bias statistic, given that returns are assumed to be normally distributed and the risk forecasts are accurate, be equal to one?
Everywhere I have read, this is just given as an article of faith but I am just not able to wrap my head around it. Can someone please help me understand why is this true?
If $r_t\sim N(\mu, \sigma)$, where $\sigma$ is the "true" standard deviation of $r_t$ (no $t$ subscript), then $\dfrac{r_t}{\sigma}\sim N(\mu, 1)$.
Assuming perfect risk forecasts (i.e. $\sigma_t = \sigma$ for all $t$), we get $\text{Std}\left(\dfrac{r_t}{\sigma_t}\right) = \text{Std}\left(\dfrac{r_t}{\sigma}\right) = 1$.
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2019-10-19 17:12:34
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https://physics.stackexchange.com/questions/215984/an-apparent-contradiction-to-m-m-0-sqrt1-v2-c2
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# An apparent contradiction to $m = m_0/\sqrt{1-v^2/c^2}$ [duplicate]
Using theoretical framework of the special relativity, we can show that the quantity that we classically regard as energy does have a property of inertia. And particularly, if the total energy of a box is $L$ then its inertia is $L/c^2$. Now suppose I have an infinitely large parallel plate capacitor which is at rest in an inertial frame $O$. Uniformly charged plates of the capacitors have such a charge density so that the uniform electric field between the plates is $E$.
Now in a frame of reference $O'$ which is moving uniformly along the area vector of the plate plane with respect to $O$, the electric field will be $E$ and magnetic field would still remain zero.
In $O$ frame, the total energy of capacitor is $L_1 = l_0 \int\frac{1}{2}\epsilon_0E^2 dA$ and thus its mass is $m_1 = L_1/c^2$.Where $l_0$ is the perpendicular separation between the plates and $dA$ is the infinitesimal small area element of one of the plates in $O$ frame.
In $O'$ frame, the total energy of the capacitor is $L_2 = l_0\sqrt{1-v^2/c^2} \int\frac{1}{2}\epsilon_0E^2 dA$ . The infinitesimal $dA$ and limits of integration remain exactly the same because no length contraction happen in the direction perpendicular to the relative motion. Here also the mass is thus $m_2 = L_2/c^2$.
So, $m_2$ = $m_1$ $\sqrt{1-v^2/c^2}$. But in general, in relativity we prove that $m = m_0/\sqrt{1-v^2/c^2}$. So why does this apparent contradiction is happening? Does it have to do anything with the fact that actually both the $m_1$ and $m_2$ are infinities? Because I doubt that it might be the case that we cannot directly write $m_2$ = $m_1$ $\sqrt{1-v^2/c^2}$ because $m_2$ and $m_1$ are infinities. But on the other hand that relation seems to hold pretty well from their corresponding expressions in the integral form.
## marked as duplicate by Community♦Nov 1 '15 at 20:16
• Treating $m[1 - \beta^2]^{-1/2}$ as inertia has problems from the very beginning. It is the correct inertia for forces acting transverse to the direction of relative motion, but is not correct for longitudinal forces. – dmckee Nov 1 '15 at 18:53
• @dmckee But while proving the $m = m_0/\sqrt{1-v^2/c^2}$ relation, we analyse a collision which has longitudinal forces. Can you suggest the reason why the expression shouldn't hold for some cases? – Dvij Mankad Nov 1 '15 at 19:02
• @dmckee Can you provide some link where I can read the relevant literature on the problems with $m_0/\sqrt{1-v^2/c^2}$ expression? – Dvij Mankad Nov 1 '15 at 19:06
• mass is velocity-independent. $m=\gamma m_0$ is a historical mistake, and shouldnt be taken seriously in any context. – AccidentalFourierTransform Nov 1 '15 at 19:26
• @qftishard I know in recent literature we consider rest mass to be the mass. And rest mass is obviously velocity independent. But are you suggesting that the inertia of a body doesn't change with the speed? I think then it creates a lot of problems with momentum conservation in the relativistic context. Can you provide some web link to read about what you are suggesting? – Dvij Mankad Nov 1 '15 at 19:35
Using theoretical framework of the special relativity, we can show that the quantity that we classically regard as energy does have a property of inertia.
It's isn't as straightforward as having a scalar $m$ like in $\vec F=m\vec a.$ And if you have mechanical momentum like $\vec p=\vec vE/c^2$ then mass doesn't appear at all and $d\vec p/dt$ has to definitely adjust the energy and maybe the velocity or the speed too. But since the energy depends on the full 3d motion you don't get the simple separation of changes in velocity components for each of the three components like you do in Newtonian mechanics. But you can get a nice change in momentum.
No word games can change that momentum can steadily increase while energy and/or velocity can be a more complicated change.
And particularly, if the total energy of a box is $L$ then its inertia is $L/c^2$.
That's a pretty big claim. If it weren't so vague I'd say its provably wrong.
In $O$ frame, the total energy of capacitor is $L_1 = l_0 \int\frac{1}{2}\epsilon_0E^2 dA$ and thus its mass is $m_1 = L_1/c^2$.
That's not true. A capacitor has massive plates and charges and such and some stress holding all the charges together and so there is more energy than the fields, and there is stress so there is more than just energy.
In $O'$ frame, the total energy of the capacitor is $L_2 = l_0\sqrt{1-v^2/c^2} \int\frac{1}{2}\epsilon_0E^2 dA$ .
Now there is kinetic energy of the massive charges too, and the stress is involved as well.
Here also the mass is thus $m_2 = L_2/c^2$.
No. Mass isn't just energy divided by $c^2$ you need the total energy (not just some of it) and you need the momentum (and in this frame there is momentum for the charges).
But in general, in relativity we prove that $m = m_0/\sqrt{1-v^2/c^2}$.
That's not true either. Sure if the total energy momentum vector exists and is timelike then there is a center of momentum frame and in that frame there is an energy and if you divide that by $c^2$ you can call that the rest mass of the system. And then you can compare the total energy in other frames to that energy and it will be larger in the other frames.
But the spatial integral of the field energy is not the total energy and it isn't the time component of the total energy momentum of a system. And a good way you can tell physically is ...
There is no rest frame or center of momentum frame for a bare electric field with no charges.
So clearly the field energy isn't a tine component of a timelike vector. Which you can tell by the fact that there isn't a fixed frame where it is smaller than any other frame.
So why does this apparent contradiction is happening?
There is no contradiction. The energy of a bare electric field simply doesn't transform the way you claimed it does. No one said it did.
Were you expecting field energy to have a mass all by itself?
You did completely ignore whatever force is keeping those charged plates from slamming into each other (you ignored it in both frames), and that force has some energy too.
Does it have to do anything with the fact that actually both the $m_1$ and $m_2$ are infinities?
No. You could talk about finite sized capacitors. Or even do a calculation in a finite universe, such as a universe that is infinite in z the direction but if you go in the x or y directions it repeats Pac Man style.
The key is to avoid the bad physics. And just like two frames can disagree about which objects have kinetic energy, you must include absolutely every bit of energy, the stress of the plates and wires, the energy of the fields, the kinetic energy and rest energy of the parts of the plates, everything.
• Special relativity suggests that mass indicates the energy content of the body. The 'useful' mass is rest mass which is by definition invariant. But still there exists a quantity called relativistic mass which is not a lorentz scalar. Also, if relativistic mass of a body is $m$ then it essentially means that the total energy of the body is $mc^2$. Total energy of a body transforms as $E = E_0/\sqrt{1-v^2/c^2}$ and so does the relativistic mass. – Dvij Mankad Nov 2 '15 at 12:47
• @Dvij Be intellectually honest. Don't pretend that using two words (energy and relativistic mass) for the same thing is an accomplishment or any kind of insight. Call it energy and move on with your life. Special relativity didn't "indicate" that you should make up two words for the same thing and call it an accomplishment. You say there is a thing called relativistic mass and I say there is a thing called energy. But the point is you can't just take equations and replace mass with energy and expect it to now be correct, that's wrong. Momentum conservation works if you use correct equations. – Timaeus Nov 2 '15 at 12:59
• @Dvij Just a bit of advice: If you consider a system of two objects, and increase that system's rest mass by accelerating the two objects to opposite directions, then you are effectively using relativistic mass but nobody can complain! ;) – stuffu Nov 2 '15 at 13:23
• @user7027 In the specific question the OP asked, we can and do complain. Ignoring some of the stress or momentum or energy does give wrong answers. Just as two objects with relative velocity can have different parts have kinetic energy depending on frame so can different energies of different parts be important to the total energy of a system. The OP is definitely making mistakes and playing semantic games won't fix it, the OP needs to actually learn relativity and track all the energy, stress, and momentum instead of picking and choosing. – Timaeus Nov 2 '15 at 13:35
• I am not telling total energy of the entire "capacitor+assembly holding capacitor plates" to be the integration of $\frac{1}{2}\epsilon_0E^2$. But I am particularly choosing the system consisting of only the fields between the plates. – Dvij Mankad Nov 2 '15 at 14:56
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2019-08-24 10:09:00
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https://mathoverflow.net/tags/inequalities/hot
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# Tag Info
24
The class of concentration of measure inequalities is a fundamental tool in modern probability (and any field that uses probability, e.g., random matrix theory, theoretical computer science, statistics, high-dimensional geometry, combinatorics, etc.). As explained in this blog post of Scott Aaronson, these are basic ways in which one "upper bounds the ...
15
Gaussian Jensen's inequality: Let $\boldsymbol{X}=(X_{1}, \ldots, X_{n})\sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol\Sigma)$ be a gaussian vector. The inequality $$\mathbb{E} B(f_{1}(X_{1}), \ldots, f_{n}(X_{n})) \leq B(\mathbb{E}f_{1}(X_{1}), \ldots, \mathbb{E}f_{n}(X_{n}))$$ holds for all real valued (test functions) $f_{1}, \ldots, f_{n}$ if and only ...
9
An LMFDB search for curves with many integer points turns up the curve 20888a1: $y^2 = x^3 - 52 x + 100$ which has $52$ integral points, a bit more than your conjectured bound of about $47.052$ using $(M_x, M_y) = (12214, 1349854)$. It does seem to be true that curves with many integer points tend to have a few large ones, but I don't know of any ...
8
$$\|\sqrt{A+B}Cx\|^2=(\sqrt{A+B}Cx,\sqrt{A+B}Cx)=\\ ((A+B)Cx,Cx)=(ACx,Cx)+(BCx,Cx)=\|\sqrt{A}Cx\|^2+\|\sqrt{B}Cx\|^2,$$ taking the supremum over unit vectors $x$ we get $$\|\sqrt{A+B}C\|^2\leqslant \|\sqrt{A}C\|^2+\|\sqrt{B}C\|^2\leqslant (\|\sqrt{A}C\|+\|\sqrt{B}C\|)^2.$$
7
Write $$G=\left( \begin{array}{ccc} a & b & c \\ b & d & e \\ c & e & f \\ \end{array} \right)$$ and, without loss of generality, $$U=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & u & 0 \\ 0 & 0 & v \\ \end{array} \right),$$ where $u,v>0$. Then $$\text{Tr}(GUGU^{-1})-\text{Tr}(G^2) =\frac{b^2 (u-1)^2 v+... 6 Strichartz estimates, which originated from Strichartz, Robert S., Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44, 705-714 (1977). ZBL0372.35001, are a family of inequalities that provide L^p (or Sobolev) type control of solutions of linear dispersive or wave equations (such as the ... 6 This is from Garding. Let P\in{\mathbb R}[X_1,\ldots,X_d] be a homogeneous polynomial. Assume that it is hyperbolic in some direction e\in{\mathbb R}^d (with say the normalisation P(e)=1) and let \Gamma be its cone of future, that is the connected component of e in the complement of \{P=0\}. It is known that \Gamma is convex. Then we have the ... 6 For any unit vector x\in L^2(\mathbb{R}^n),$$\|\sqrt{A+B}\,Cx\|^2=(\sqrt{A+B}\,Cx,\sqrt{A+B}\,Cx) =(ACx,Cx)+(BCx,Cx)=\|\sqrt A\,Cx\|^2+\|\sqrt B\,Cx\|^2 \le(\|\sqrt A\,Cx\|^2+\|\sqrt B\,Cx\|)^2 \le(\|\sqrt A\,C\|+\|\sqrt B\,C\|)^2.$$So,$$\|\sqrt{A+B}\,C\|\le\|\sqrt A\,C\|+\|\sqrt B\,C\|.$$4 For any real numbers u,v,c such that u\le c\le v, let \mu_{c;u,v} denote the unique probability distribution on the set \{u,v\} with mean c. Your generalization of Jensen's inequality follows immediately from the well-known fact that any probability distribution \mu on \mathbb R with a given mean c\in\mathbb R is a mixture of probability ... 4 I came across this inequality on the Gaussian space recently. I was not aware of its existence since it is not really a classical one in comparison to the Poincaré inequality or the Logarithmic Sobolev inequality but it seems to be useful in order to prove the analyticity of the Ornstein-Uhlenbeck semigroup in L^p(\gamma). Let \gamma be the standard ... 4 Suppose we have such an n where P(n) is false. Now define (a, b, c) := (1, n(n-2), (n-1)^2) and observe that these three numbers are pairwise coprime and satisfy a + b = c. Then we have:$$ \textrm{rad}(abc) = \textrm{rad}(n(n-1)^2(n-2)) = \textrm{rad}(n(n-1)(n-2)) \leq n $$Moreover, the radical of n(n-1)(n-2) cannot be equal to any of n, n-1... 3 A really simple but powerful inequality is the so-called improved Kato inequality. I first learned about it when I was studying Uhlenbeck's removable singularity theorem for self-dual Yang-Mills connections. However, when I explained the inequality to Duong Phong and Eli Stein in Phong's office, Stein reacted with "It's in my book! It's in my book!"... 3 Concerning your first question: Let p_k:=P(B_{n,p}=k). We have to show that \begin{equation*} p_k-p_{k+1}\ll\frac1{npq}, \tag{1} \end{equation*} where q:=1-p and a\ll b means that a\le Cb for some universal real constant C>0. Clearly, without loss of generality (wlog) \begin{equation*} 1\ll npq. \end{equation*} Since p_{k+1}=\frac{n-k}{k+... 3 Esseen's anti concentration inequality is the basis of a lot of relatively recent (past 10-15 years) work on non asymptotic random matrix theory, particularly results on the smallest singular values of many random matrix models. It states that if Y is a real valued random variable, then$$\sup_{t \in \mathbb{R}} \mathbb{P}(|Y-t| \le 1)\le \int_{-2}^2 |\...
2
The expander Chernoff bound is a particularly nice generalization of the Chernoff inequality that is not so well known. It states the following: Let $G = (V,E)$ be a regular graph and consider a function $f : V \rightarrow [0,1]$. Perform a random walk $v_1, \cdots, v_t$ on $G$ by first picking $v_1$ uniformly at random. Then $$\mathbb{P}\left(\frac{1}t \... 2 I will assume c\le 2, since that seems to be the case you are interested in. The argument below is formulated in terms of taking a given c and computing the optimal \alpha, but this is equivalent to your question and the result agrees with your conjecture. Step 1: We can change the formulation of the question so that the weights can be any nonnegative ... 2 I will more comfortable with the notation v_\epsilon=\hat{u_\epsilon}; you have then$$ v_\epsilon(t,x)=\alpha(t,x)+\int_0^t\int e^{2πix(\xi+\epsilon\phi(s,\xi))} \hat{v_\epsilon}(s,\xi) d\xi ds=\alpha(t,x)+\int_0^t \bigl(\textrm{Op}(e^{2πix\epsilon\phi(s,\xi)}) v(s,\cdot)\bigr) (x) ds $$where \textrm{Op}(e^{2πix\epsilon\phi(s,\xi)})=A_{\epsilon, s} is ... 1 We have 0\le a\le b\le1 and T\in(0,\infty). We want to know when there is a positive constant C such that$$\int_0^T dt\, \int_a^b dx\, u^2(x-t)\geq C\int_0^1 dx\,u^2(x) \tag{1}$$for all measurable functions u\colon\mathbb R\to\mathbb R such that u(x)=0 for x\notin(a,b). The answer is: never. Indeed, without loss of generality a<b. The left-... 1 Let l(a,b) denote the left-hand side of both inequalities. Then l(b,a)=l(a,b)=l(-a,-b). The right-hand sides of both inequalities have the same properties. So, without loss of generality (wlog) a\ge b and a\ge0. Also, by homogeneity, wlog a=1. So, we have these two cases to consider:$$(i)\ 0\le b\le a=1\quad\text{and}\quad (ii)\ b<0<a=1. ...
1
I am not a professional mathematician, thus feel free (you or your colleagues/professors of the site) tell me if my answer doesn't fit with your requirements that I can to delete it. An important inequality in complex analysis and functional analysis is the statement of Hadamard three-lines theorem, see the section Statement from this link of the Wikipedia ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2020-07-13 12:27:50
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https://www.weak-learner.com/blog/2019/11/03/gmail-smart-compose/
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# Gmail Smart Compose: Real-Time Assisted Writing
### Overview
• A system for providing real-time, interactive suggestions to help users compose messages quickly and with confidence in Gmail.
• Challenges include latency (90th percentile is 60 ms (<100ms)), scale (1.5 billion users), personalization, fairness and privacy and Metrics Design (offline metrics correlate with online).
### Architecture
Data
• Previous E-Mail
• Subject
• Date & time (discrete)
• Locale
Preprocessing
• Language Detection (strip text not in language)
• Segmentation & Tokenization - sentence boundaries detected, sentences are broken down into words and punctuation marks.
• Normalization - Infrequent words and entities like name, email, URL and phone numbers are replaced by special tokens.
• Quotation Removal - quoted original message is removed.
• Salutation/Close Removal
Models
• In LM-A: Input sequence (to LM) is the prefix of the current e-mail. The context is encoded using a dedicated encoder (average word-embeddings) and is concatenated at each time step of the LM.
• In LM-B: Input sequence is concatenation of (subject, previous email, current e-mail) with some special token to delimit them. Much simpler but longer sequence.
• In Seq2Seq Model: The encoder is subject and previous email body and the decoder is current email body.
Triggering
• Generate n-best predictions/candidates using beam search.
• Each candidate sequence is considered complete when a sentence punctuation token or a special end-of-sequence () token is generated, or when the candidate reaches a predefined maximum output sequence length.
• Length-normalized log conditional probability as the confidence score of each suggestion sequence and define a triggering threshold based on a target triggering frequency/coverage.
Eval
• Log Perplexity
• ExactMatch@N - In this paper, we report an averaged ExactMatch number by weighted averaging the ExactMatch for all the lengths up to 15.
Production System
• Context Encoding - Cached and stored only once.
• Prefix Encoding - Takes hidden layer and current text. User is assigned to a fixed server, so directly proportional to text typed since last request.
• Beam Search - Takes in various parameters to control beam search (number of steps, valid tokens to end consideration of a beam, and blacklisted words). We can also filter for partial match.
Personalization
• Train for each user a light-weight language model adapted to the user’s personal mail data.
• n-gram language model with Katz-backoff stored using compact weighted finite automata (WFA) format.
\begin{align*} P_{final} = \alpha P_{personal} + (1 - \alpha) * P_{global} \end{align*}
Multi-lingual Model
• Using multilingual wordpiece for ease of maintenance.
### Results
RNN Layers
• Use LSTM and residual connections between consecutive layers.
• Uniform Label Smoothing
Transformer
• Same as Vaswani et al
• We observed that for the LSTM-2-1024, simply by joining the averaged embeddings from subject and previous e-mail to the model input reduces the test log perplexity by 0.13, showing that contextual information indeed helps improving model quality.
• We can see that the LSTM seq2seq model outperforms the LSTM language models with similar number of model params, indicating that an encoder-decoder architecture with attention is more effective in modeling the context information.
Future Work
• Adapted version of the Transformer model where self-attention is applied locally over a fixedsized window of steps during decoding, instead of over all previous decoding steps
• Pretrained language models.
• Use VAE.
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2020-09-29 13:24:28
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https://scicomp.stackexchange.com/questions/38969/algorithm-for-solving-systems-which-are-nearly-symmetric-adjoint
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# Algorithm for solving systems which are nearly symmetric/adjoint?
I am familiar with Cholesky decomposition and LU factorization for solving systems of linear equations.
I have a problem where I have large sparse matrices (say, 1000x1000 or larger) where only one or two rows/columns (last couple rows/columns) break symmetry. I understand that Cholesky is nearly twice as efficient as LU, but I can't use Cholesky due to these outlier rows/columns.
Is there another method or algorithm that can handle this particular case - i.e., take advantage of the fact that nearly the entire matrix is self-adjoint/symmetric (real values only here)?
• Performing an LU decomposition $O(2/3 n^{3})$ on a system with $O(n)$ entries is over expensive. As a consequence, Stationary method such as Jacobi iteration, Gauss-Seidel, and SOR method were developed but these methods were popular in 1950s and are considered old-fashion. Now you could resort to the highly advanced Krylov methods to solve sparse systems. On MATLAB you can use the command bicgstab() to solve this sparse system mathworks.com/help/matlab/ref/bicgstab.html Aug 22 at 10:35
• Various strategies come to mind, including the one suggested in @StevenRoberts 's answer and Schur complements, but I think that the real challenge is coming up with something that is provably stable (or, at least, as unstable as solving the original system with LU factorization): if at any point you invert another matrix instead of $A$, that matrix may be ill-conditioned. Aug 22 at 19:41
Let's express the matrix $$A \in \mathbb{R}^{n \times n}$$ with which we want to solve linear systems as $$A = S + U V$$ where $$S$$ is a symmetric matrix, $$U \in \mathbb{R}^{n \times r}$$, and $$V \in \mathbb{R}^{r \times n}$$. That is, $$U V$$ is a low rank update to account for the lack of symmetry. From your question, it appears $$r$$ is just 1 or 2.
The Woodbury matrix identity tells us that $$A^{-1} x = (I_{n \times n} - \underbrace{S^{-1} U (I_{r \times r} + V S^{-1} U)^{-1}}_{W} V) S^{-1} x = (I_{n \times n} - W V) S^{-1} x.$$ Now, inverses appear for the symmetric matrix $$S$$. During the preprocessing step, you can compute the Cholesky factorization of $$S$$ and precompute $$W = S^{-1} U (I_{r \times r} + V S^{-1} U)^{-1}$$. Note that $$W$$ only requires $$\mathcal{O}(r n^2)$$ flops to compute, and that should be neglidgible.
After preprocessing, a linear system can be solved with $$(I_{n \times n} - W V) S^{-1} x$$. Working right to left, we can use forward/back substitution to compute $$S^{-1} x$$. Then, we need to perform a matrix-vector multiplication with $$\left( I_{n \times n} - W V \right)$$. At a cost of $$\mathcal{O}(r n)$$, that is neglidgible.
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2021-12-04 01:35:36
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http://openstudy.com/updates/560a2785e4b032660b2113e0
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## anonymous one year ago Prove that every simple function f(x) can be written in a form: f(x) = sum from n=1to N of αnχAi(x), sets Ai being mutually disjoint and αn not equals αn0 when n not equals n0, N < ∞.
1. anonymous
$\sum_{n=1}^{N} an XAi(x)$
2. anonymous
Unfortunately my entire response got deleted, but here we go again x_x This isn't a proof, more of just an idea and applying that idea in a basic case. But try thinking of it from the point of view of a step function. As you probably know, a step function can be written as: $\sum_{n=1}^{N}a_{k}\mathcal{X}_{R_{k}}(x)$ where each $$R_{k}$$ is a rectangle. If your rectangles are not disjoint, like in a basic example like this: |dw:1443516783423:dw| Clearly the intervals are not disjoint. But we can always refine the intervals to make them disjoint while still maintaining the value of the step function. (Just for reference, the lebesgue integral of this step function would give a value of 4(3) + 1(2) = 14). Wherever we have overlap, we will just add the values along that interval and rewrite as a single constant times the characteristic. In the picture, the step function can be written as: $$\phi = 4\mathcal{X}_{[0,3]} + \mathcal{X}_{[2,4]}$$ On the overlap, which occurs on [2,3], we add the values, which gives us 5, and rewrite that interval as 5 times the characteristic on that interval. Thus our step function can be rewitten like this: $$\phi = 4\mathcal{X}_{[0,2]} + 5\mathcal{X}_{(2,3]} + \mathcal{X}_{(3,4]}$$ Now we have the step function rewritten such that each (R_{k}\) is disjoint. (And the lebesgue integral gives us the same value 4(2) + 5(1) + 1(1) = 14). See if you can apply that idea to your simple functions. Of course now you're dealing with arbitrary measurable sets, but the idea is the same. How can you rewrite two sets that may overlap as a union of disjoint sets?
3. anonymous
$\sum_{n=1}^{N}a_{n}\mathcal{X}_{R_{n}}$ I meant this of course. Sorry about mixing k in there, not meant to be there of course.
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2017-01-21 15:35:09
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https://stats.stackexchange.com/questions/380377/doing-regression-only-with-correlation-matrix-means-and-sds
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# Doing regression only with correlation matrix, means, and SDs [duplicate]
I was wondering how mathematically is it possible to run a full regression analysis between 3 predictors (x1 x2 x3) and a dependent variable (y) by only knowing the: Means, Ns, SDs, and the Correlations between all these 4 variables (without the original data)?
I highly appreciate an R demonstration.
ns <- c(273, 273, 273, 273)
means <- c(15.4, 7.1, 3.5, 6.2)
sds <- c(3.4, 0.9, 1.5, 1.4)
r <- matrix( c(
1.0, .57, -.4, .48,
.57, 1.0, -.61, .66,
-.4, -.61, 1.0, -.68,
.48, .66, -.68, 1.0), 4)
rownames(r) <- colnames(r) <- c('y', paste0('x', 1:3))
• You cannot run a truly "full" regression analysis with just these statistics, because you will not be able to construct residuals and perform regression diagnostics that depend on them. You are limited to making and testing parameter estimates.
– whuber
Dec 5, 2018 at 14:35
• Structural equation modeling is the most obvious answer in my mind, which is more or less the math provided in the answer below. Most SEM programs will be able to accept your inputs (all need to be able to estimate a covariance matrix in the end). Dec 10, 2018 at 2:29
• @whuber, do I need to first convert my correlation matrix into a var-covariance matrix using r_x_iy_i * sd_x_i*sd_y_i and then go from there? Dec 10, 2018 at 4:52
• That's one approach, because it reduces your problem to one with a known, explicit solution.
– whuber
Dec 10, 2018 at 15:13
$$\left(\begin{matrix} 1.00 & -0.61 & 0.66\\ -.61 & 1.00 & -0.68\\ .66 & -.68 & 1.00\end{matrix}\right)^{-1}\left(\begin{matrix} 0.57\\ -.40\\ .48\end{matrix}\right)$$
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2022-08-14 03:52:25
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https://boards.fireden.net/co/thread/109641258/
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170KiB, 536x411, hrnn34.png
## Danger Mouse!
No.109641258
Dah dahdahdah dah dahdah daaahhhh! This thread's the greatest, this thread's fantastic, whenever we need to discuss Danger Mouse it will be there!
...Okay maybe that was the worst intro to a thread ever, heheh! Oh well, let's talk about DM and how awesome he is! And, of course, I'll be posting theories and stuff too!
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2021-09-24 12:03:15
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https://msp.org/ant/2010/4-8/p06.xhtml
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Vol. 4, No. 8, 2010
Download this article For screen For printing
Recent Issues
The Journal About the Journal Editorial Board Subscriptions Editors' Interests Submission Guidelines Submission Form Editorial Login Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Remarks on modular symbols for Maass wave forms
Yuri I. Manin
Vol. 4 (2010), No. 8, 1091–1114
Abstract
In this paper I introduce modular symbols for Maass wave cusp forms. They appear in the guise of finitely additive functions on the boolean algebra generated by intervals with nonpositive rational ends, with values in analytic functions (pseudomeasures in the sense of Manin and Marcolli). We explain the basic issues and draw an analogy with the $p$-adic case. We then construct the new modular symbols, followed by the related Lévy–Mellin transforms. This work builds on the fundamental study of Lewis and Zagier (2001).
To Professor F. Hirzebruch, with friendship and admiration, for his anniversary.
Keywords
Maass modular forms, modular symbols
Primary: 11F37
Milestones
Received: 12 January 2010
Accepted: 1 October 2010
Published: 24 February 2011
Authors
Yuri I. Manin Max-Planck-Institut für Mathematik Vivatsgasse 7 D-53111 Bonn Germany Department of Mathematics Northwestern University Evanston, IL 60208-2730 United States
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2019-11-17 18:41:47
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https://socratic.org/questions/5710be2b11ef6b3450210436
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Question 10436
Apr 15, 2016
${\text{0.452 mol L}}^{- 1}$
Explanation:
In order to be able to calculate this solution's molarity, you must first determine how many moles of ethanol, $\text{C"_2"H"_5"OH}$, are present in that $\text{1.77-g}$ sample.
To do that, use ethanol's molar mass, which is equal to ${\text{46.07 g mol}}^{- 1}$. As you know, a compound's molar mass tells you the mass of one mole of that compound.
In this case, one mole of ethanol has a mass of $\text{46.07 g}$, which means that your sample will contain
1.77 color(red)(cancel(color(black)("g"))) * ("1 mole C"_2"H"_5"OH")/(46.07color(red)(cancel(color(black)("g")))) = "0.03842 moles C"_2"H"_5"OH"
Now, a solution's molarity tells you how many moles of solute you get per liter of solution. This means that you can find a solution's molarity by finding out how many moles of solute you get in one liter of solution.
Your solution is said to have a volume of $\text{85.0 mL}$. Convert this to liters by using
$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 L" = 10^3"mL}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
85.0 color(red)(cancel(color(black)("mL"))) * "1 L"/(10^3color(red)(cancel(color(black)("mL")))) = 85.0 * 10^(-3)"L"
So, the number of moles of solute present in one liter of this solution will be
1 color(red)(cancel(color(black)("L solution"))) * ("0.03842 moles C"_2"H"_5"OH")/(85.0 * 10^(-3)color(red)(cancel(color(black)("L solution")))) = "0.452 moles C"_2"H"_5"OH"
Since one liter of solution contains $0.452$ moles of ethanol, it follows that the solution's molarity will be equal to
"molarity" = c = color(green)(|bar(ul(color(white)(a/a)"0.452 mol L"^(-1)color(white)(a/a)|)))#
The answer is rounded to three sig figs.
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2019-12-14 15:29:39
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https://www.zora.uzh.ch/id/eprint/108317/
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# A study of CP violation in B±→DK± and B±→Dπ± decays with D→K0SK±π∓ final states
LHCb Collaboration; Bernet, R; Müller, K; Steinkamp, O; Straumann, U; Vollhardt, A; et al (2014). A study of CP violation in B±→DK± and B±→Dπ± decays with D→K0SK±π∓ final states. Physics Letters B, 733:36-45.
## Abstract
A first study of CP violation in the decay modes B±→[K0SK±π∓]Dh± and B±→[K0SK∓π±]Dh±, where h labels a K or π meson and D labels a D0 or D⎯⎯⎯0 meson, is performed. The analysis uses the LHCb data set collected in pp collisions, corresponding to an integrated luminosity of 3 fb−1. The analysis is sensitive to the CP-violating CKM phase γ through seven observables: one charge asymmetry in each of the four modes and three ratios of the charge-integrated yields. The results are consistent with measurements of γ using other decay modes.
## Abstract
A first study of CP violation in the decay modes B±→[K0SK±π∓]Dh± and B±→[K0SK∓π±]Dh±, where h labels a K or π meson and D labels a D0 or D⎯⎯⎯0 meson, is performed. The analysis uses the LHCb data set collected in pp collisions, corresponding to an integrated luminosity of 3 fb−1. The analysis is sensitive to the CP-violating CKM phase γ through seven observables: one charge asymmetry in each of the four modes and three ratios of the charge-integrated yields. The results are consistent with measurements of γ using other decay modes.
## Statistics
### Citations
Dimensions.ai Metrics
20 citations in Web of Science®
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### Altmetrics
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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Physics Institute 530 Physics English 2014 20 Feb 2015 21:57 06 Dec 2019 08:29 Elsevier 0370-2693 Gold Publisher DOI. An embargo period may apply. https://doi.org/10.1016/j.physletb.2014.03.051
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2020-01-23 19:53:31
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https://www.williamstein.org/papers/ant/html/node90.html
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# Exercises
1. Let .
1. Find invertible integer matrices and such that is in Smith normal form.
2. What is the group structure of the cokernel of the map defined by multiplication by ?
2. Let be the abelian group generated by with relatoins and . Find a product of cyclic groups that is isomorphic to .
3. Prove that each of the following rings have infinitely many prime ideals:
1. The integers . [Hint: Euclid gave a famous proof of this long ago.]
2. The ring of polynomials over .
3. The ring of polynomials over .
4. The ring of all algebraic integers. [Hint: Use Zorn's lemma, which implies that every ideal is contained in a maximal ideal. See, e.g., Prop 1.12 on page 589 of Artin's Algebra.]
4. (This problem was on the graduate qualifying exam on Tuesday.) Let denote the subset of all elements of that satisfy a monic polynomial with coefficients in the ring of integers. We proved in class that is a ring.
1. Show that the ideals and in are distinct.
2. Prove that is not Noetherian.
5. Show that neither nor is a unique factorization domain. [Hint: Consider the factorization into irreducible elements of in the first case and in the second. A nonzero element in a ring is an irreducible element if it is not a unit and if whenever , then one of or is a unit.]
6. Find the ring of integers of each of the following number fields:
1. ,
2. , and
3. .
Do not use a computer for the first two.
7. Find the discriminants of the rings of integers of the numbers fields in the previous problem. (Do not use a computer.)
8. Let be a finite integral domain. Prove that is a field. [Hint: Show that if is a nonzero element, then has an inverse by considering powers of .]
9. Suppose is a tower of number fields and let be a field embedding of into that fixes elementwise. Show that extends in exactly ways to a field embedding .
1. Suppose and are principal ideals in a ring . Show that the set is an ideal.
2. Give an example of ideals and in the polynomial ring in two variables such that is not an ideal. Your example illustrates why it is necessary to define the product of two ideals to be the ideal generated by .
3. Give an example of a ring of integers of a number field, and ideals and such that is not an ideal.
1. Let be a field. Prove that is a Dedekind domain.
2. (Problem 1.12 from Swinnerton-Dyer) Let be an indeterminate. Show that the ring is Noetherian and integrally closed in its field of fractions, but is not a Dedekind domain.
10. Use to write each of the following (fractional) ideals as a product of explicitly given prime ideals:
1. The ideal in .
2. The ideals and in the ring of integers of , where is a root of the irreducible polynomial . (The field is called the th cyclotomic field.)
3. The principal fractional ideal in .
11. Suppose is an order in the ring of integers of a number field. (Recall that an order is a subring of finite index in .) For each of the following questions, either explain why the answer is yes for any possible order in any , or find one specific counterexample:
1. Is necessarily Noetherian?
2. Is necessarily integrally closed in its field of fractions?
3. Is every nonzero prime ideal of necessarily maximal?
4. Is it always possible to write every ideal of uniquely as a product of prime ideals of ?
12. Let be the ring of integers of a number field . Prove that the group of fractional ideals of , under multiplication is (non-canonically) isomorphic to the group of positive rational numbers under multiplication.
1. Suppose is a number field of degree . Prove that for some .
2. Prove that if and are two number fields of degree and then .
13. (*) Does there exist a number field of degree such that for all ? If so, give an explicit example.
14. Let be the quintic number field generated by a root of . Draw a diagram (be creative) that illustrates the factorization of every prime , with , in .
15. (Problem 1.9 in Swinnerton-Dyer) Show that the only solutions to are given by , as follows. Factor the equation in the number field , which has class number . Show that if is an integer solution then the ideal must be the cube of an ideal, and hence ; thus .
16. Suppose and are ideals in the ring of integers of a number field . Does ? Prove or give a counterexample.
17. Let be the ring of integers , and let
and
be integral ideals of .
1. Find an element of that is congruent to modulo and is congruent to modulo .
2. What is the cardinality of ?
3. Find an element such that is coprime to .
18. Let be the ring of integers of a number field , and suppose has exactly complex embeddings. Prove that the sign of is .
19. (*) Suppose is an order in the ring of integers of a number field. Is every ideal in necessarily generated by two elements? (Answer: No. Challenge: Given an example.)
20. Find representative ideals for each element of the class group of . Illustrate how to use the Minkowski bound to prove that your list of representatives is complete.
21. Suppose is an order in the ring of integers of a number field. Is every ideal in necessarily generated by two elements?
22. Let be a number field of degree with pairs of complex conjugate embeddings. Prove that
23. Do the exercise on page 19 of Swinnerton-Dyer, which shows that the quantity in the finiteness of class group theorem can be taken to be .
24. Let denote a root of and let . Show that and that has class number (don't just read this off from the output of the commands MaximalOrder and ClassNumber). [Hint: consider the square factors of the discriminant of and show that is an algebra integer if and only if , , and are all even.]
25. If is a closed, bounded, convex, symmetric set in with , for some positive integer , show that contains at least nonzero points in .
26. Prove that any finite subgroup of the multiplicative group of a field is cyclic.
27. For a given number field , which seems more difficult for to compute, the class groups or explicit generators for the group of units? It is very difficult (but not impossible) to not get full credit on this problem. Play around with some examples, see what seems more difficult, and justify your response with examples. (This problem might be annoying to do using the web page, since it kills your job after 30 seconds. Feel free to request a binary of from me, or an account on MECCAH (Mathematics Extreme Computation Cluster at Harvard).)
1. Prove that there is no number field such that .
2. Is there a number field such that ?
28. Prove that the rank of is unbounded as varies over all number fields.
29. Let .
1. Show that and .
2. Find explicitly generators for the group of units of (you can use for this).
3. Draw an illustration of the log map , including the hyperplane and the lattice in the hyperplane spanned by the image of .
30. Find the group of units of as an abstract group as a function of . (I.e., find the number of cyclic factors and the size of the torsion subgroup. You do not have to find explicit generators!)
31. Let , where is a root .
1. Show that .
2. Find explicitly the log embedding of into a -dimensional hyperplane in , and draw a picture.
32. Prove that if is a quadratic field and the torsion subgroup of has order bigger than , then or .
33. A is a real algebraic integer, greater than 1, with the property that all of its conjugates lie on or within the unit circle, and at least one conjugate lies on the unit circle. By any method (including google''), give two examples of Salem numbers.
34. Let and let be a number field. Show that .
35. A totally real number field is a number field in which all embeddings into have image in . Prove there are totally real number fields of degree , for every prime . [Hint: Let denote a primitive th root of unity. For , show that is totally real of degree . Now prove that can be made divisible by any prime.]
36. Give an example of a number field and a prime such that the in the factorization of are not all the same.
37. Let be a number field. Give the simplest'' proof you can think of that there are only finitely many primes that ramify (i.e., have some ) in . [The meaning of simplest'' is a matter of taste.]
38. Give examples to show that for a Galois extension, the quantity can be arbirarily large and can be arbitrarily large.
39. Suppose is Galois and is a prime such that is also prime (i.e., is inert in ). Show that is a cyclic group.
40. (Problem 7, page 116, from Marcus Number Fields) For each of the following, find a prime and quadratic extensions and of that illustrates the assertion:
1. The prime can be totally ramified in and without being totally ramified in .
2. The fields and can each contain unique primes lying over while does not.
3. The prime can be inert in and without being inert in .
4. The residue field extensions of can be trivial for and without being trivial for .
41. Let by the symmetric group on three symbols, which has order .
1. Observe that , where is the dihedral group of order , which is the group of symmetries of an equilateral triangle.
2. Use (45a) to write down an explicit embedding .
3. Let be the number field , where is a nontrivial cube root of unity. Show that is a Galois extension with Galois group isomorphic to .
4. We thus obtain a -dimensional irreducible complex Galois representation
Compute a representative matrix of and the characteristic polynomial of for .
42. Let . Show that is Galois over , compute the Galois group of , and compute .
43. Let be any field. Prove that the only nontrivial valuations on which are trivial on are equivalent to the valuation (15.3.3) or (15.3.4) of page .
44. A field with the topology induced by a valuation is a topological field, i.e., the operations sum, product, and reciprocal are continuous.
45. Give an example of a non-archimedean valuation on a field that is not discrete.
46. Prove that the field of -adic numbers is uncountable.
47. Prove that the polynomial has all its roots in , and find the -adic valuations of each of these roots. (You might need to use Hensel's lemma, which we don't discuss in detail in this book. See [Cas67, App. C].)
48. In this problem you will compute an example of weak approximation, like I did in the Example 16.3.3. Let , let be the -adic absolute value, let be the -adic absolute value, and let be the usual archimedean absolute value. Find an element such that , where , , and .
49. Prove that has a cube root in using the following strategy (this is a special case of Hensel's Lemma, which you can read about in an appendix to Cassel's article).
1. Show that there is an element such that .
2. Suppose . Use induction to show that if and , then there exists such that . (Hint: Show that there is an integer such that .)
3. Conclude that has a cube root in .
50. Compute the first digits of the -adic expansions of the following rational numbers:
the 4 square roots of $41$
51. Let be an integer. Prove that the series
converges in .
52. Prove that has a cube root in using the following strategy (this is a special case of Hensel's Lemma'').
1. Show that there is such that .
2. Suppose . Use induction to show that if and , then there exists such that . (Hint: Show that there is an integer such that .)
3. Conclude that has a cube root in .
53. Let be an integer.
1. Prove that is equipped with a natural ring structure.
2. If is prime, prove that is a field.
1. Let and be distinct primes. Prove that .
2. Is isomorphic to either of or ?
54. Prove that every finite extension of comes from'' an extension of , in the following sense. Given an irreducible polynomial there exists an irreducible polynomial such that the fields and are isomorphic. [Hint: Choose each coefficient of to be sufficiently close to the corresponding coefficient of , then use Hensel's lemma to show that has a root in .]
55. Find the -adic expansion to precision 4 of each root of the following polynomial over :
Your solution should conclude with three expressions of the form
1. Find the normalized Haar measure of the following subset of :
2. Find the normalized Haar measure of the subset of .
56. Suppose that is a finite extension of and is a finite extension of , with and assume that and have the same degree. Prove that there is a polynomial such that and . [Hint: Combine your solution to 59 with the weak approximation theorem.]
57. Prove that the ring defined in Section 9 really is the tensor product of and , i.e., that it satisfies the defining universal mapping property for tensor products. Part of this problem is for you to look up a functorial definition of tensor product.
58. Find a zero divisor pair in .
1. Is a field?
2. Is a field?
59. Suppose denotes a primitive th root of unity. For any prime , consider the tensor product . Find a simple formula for the number of fields appearing in the decomposition of the tensor product . To get full credit on this problem your formula must be correct, but you do not have to prove that it is correct.
60. Suppose and are equivalent norms on a finite-dimensional vector space over a field (with valuation ). Carefully prove that the topology induced by is the same as that induced by .
61. Suppose and are number fields (i.e., finite extensions of ). Is it possible for the tensor product to contain a nilpotent element? (A nonzero element in a ring is if there exists such that .)
62. Let be the number field .
1. In how many ways does the -adic valuation on extend to a valuation on ?
2. Let be a valuation on that extends . Let be the completion of with respect to . What is the residue class field of ?
63. Prove that the product formula holds for similar to the proof we gave in class using Ostrowski's theorem for . You may use the analogue of Ostrowski's theorem for , which you had on a previous homework assignment. (Don't give a measure-theoretic proof.)
64. Prove Theorem 20.3.5, that The global field is discrete in and the quotient of additive groups is compact in the quotient topology.'' in the case when is a finite extension of , where is a finite field.
William Stein 2004-05-06
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2021-12-08 02:35:30
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|
https://www.jobilize.com/physics/section/summary-vector-addition-and-subtraction-analytical-by-openstax?qcr=www.quizover.com
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# 3.2 Vector addition and subtraction: analytical methods (Page 4/5)
Page 4 / 5
Learn how to add vectors. Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats.
## Summary
• The analytical method of vector addition and subtraction involves using the Pythagorean theorem and trigonometric identities to determine the magnitude and direction of a resultant vector.
• The steps to add vectors $\mathbf{A}$ and $\mathbf{B}$ using the analytical method are as follows:
Step 1: Determine the coordinate system for the vectors. Then, determine the horizontal and vertical components of each vector using the equations
$\begin{array}{lll}{A}_{x}& =& A\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\theta \\ {B}_{x}& =& B\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\theta \end{array}$
and
$\begin{array}{lll}{A}_{y}& =& A\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \\ {B}_{y}& =& B\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \text{.}\end{array}$
Step 2: Add the horizontal and vertical components of each vector to determine the components ${R}_{x}$ and ${R}_{y}$ of the resultant vector, $\mathbf{\text{R}}$ :
${R}_{x}={A}_{x}+{B}_{x}$
and
${R}_{y}={A}_{y}+{B}_{y.}$
Step 3: Use the Pythagorean theorem to determine the magnitude, $R$ , of the resultant vector $\mathbf{\text{R}}$ :
$R=\sqrt{{R}_{x}^{2}+{R}_{y}^{2}}.$
Step 4: Use a trigonometric identity to determine the direction, $\theta$ , of $\mathbf{\text{R}}$ :
$\theta ={\text{tan}}^{-1}\left({R}_{y}/{R}_{x}\right).$
## Conceptual questions
Suppose you add two vectors $\mathbf{A}$ and $\mathbf{B}$ . What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude? What relative direction between them produces the resultant with the smallest magnitude? What is the minimum magnitude?
Give an example of a nonzero vector that has a component of zero.
Explain why a vector cannot have a component greater than its own magnitude.
If the vectors $\mathbf{A}$ and $\mathbf{B}$ are perpendicular, what is the component of $\mathbf{A}$ along the direction of $\mathbf{B}$ ? What is the component of $\mathbf{B}$ along the direction of $\mathbf{A}$ ?
## Problems&Exercises
Find the following for path C in [link] : (a) the total distance traveled and (b) the magnitude and direction of the displacement from start to finish. In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition.
(a) 1.56 km
(b) 120 m east
Find the following for path D in [link] : (a) the total distance traveled and (b) the magnitude and direction of the displacement from start to finish. In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition.
Find the north and east components of the displacement from San Francisco to Sacramento shown in [link] .
North-component 87.0 km, east-component 87.0 km
Solve the following problem using analytical techniques: Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements $\mathbf{A}$ and $\mathbf{B}$ , as in [link] , then this problem asks you to find their sum $\mathbf{R}=\mathbf{A}+\mathbf{B}$ .)
Note that you can also solve this graphically. Discuss why the analytical technique for solving this problem is potentially more accurate than the graphical technique.
Repeat [link] using analytical techniques, but reverse the order of the two legs of the walk and show that you get the same final result. (This problem shows that adding them in reverse order gives the same result—that is, $\mathbf{\text{B + A = A + B}}$ .) Discuss how taking another path to reach the same point might help to overcome an obstacle blocking you other path.
30.8 m, 35.8 west of north
You drive $7\text{.}\text{50 km}$ in a straight line in a direction $15º$ east of north. (a) Find the distances you would have to drive straight east and then straight north to arrive at the same point. (This determination is equivalent to find the components of the displacement along the east and north directions.) (b) Show that you still arrive at the same point if the east and north legs are reversed in order.
Do [link] again using analytical techniques and change the second leg of the walk to $\text{25.0 m}$ straight south. (This is equivalent to subtracting $\mathbf{B}$ from $\mathbf{A}$ —that is, finding $\mathbf{\text{R}}\prime =\mathbf{\text{A – B}}$ ) (b) Repeat again, but now you first walk $\text{25}\text{.}\text{0 m}$ north and then $\text{18}\text{.}\text{0 m}$ east. (This is equivalent to subtract $\mathbf{A}$ from $\mathbf{B}$ —that is, to find $\mathbf{A}=\mathbf{B}+\mathbf{C}$ . Is that consistent with your result?)
(a) $\text{30}\text{.}\text{8 m}$ , $\text{54}\text{.}2º$ south of west
(b) $\text{30}\text{.}\text{8 m}$ , $\text{54}\text{.}2º$ north of east
A new landowner has a triangular piece of flat land she wishes to fence. Starting at the west corner, she measures the first side to be 80.0 m long and the next to be 105 m. These sides are represented as displacement vectors $\mathbf{A}$ from $\mathbf{B}$ in [link] . She then correctly calculates the length and orientation of the third side $\text{C}$ . What is her result?
You fly $\text{32}\text{.}\text{0 km}$ in a straight line in still air in the direction $35.0º$ south of west. (a) Find the distances you would have to fly straight south and then straight west to arrive at the same point. (This determination is equivalent to finding the components of the displacement along the south and west directions.) (b) Find the distances you would have to fly first in a direction $45.0º$ south of west and then in a direction $45.0º$ west of north. These are the components of the displacement along a different set of axes—one rotated $45º$ .
18.4 km south, then 26.2 km west(b) 31.5 km at $45.0º$ south of west, then 5.56 km at $45.0º$ west of north
A farmer wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as $\mathbf{A},$ $\mathbf{B},$ and $\mathbf{C}$ in [link] , and then correctly calculates the length and orientation of the fourth side $\mathbf{D}$ . What is his result?
In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: $2\text{.}\text{50 km}$ $45.0º$ north of west; then $4\text{.}\text{70 km}$ $60.0º$ south of east; then $1.30\phantom{\rule{0.25em}{0ex}}\text{km}$ $25.0º$ south of west; then $5\text{.}\text{10 km}$ straight east; then $1.70\phantom{\rule{0.25em}{0ex}}\text{km}$ $5.00º$ east of north; then $7\text{.}\text{20 km}$ $55.0º$ south of west; and finally $2\text{.}\text{80 km}$ $10.0º$ north of east. What is his final position relative to the island?
$7\text{.}\text{34 km}$ , $\text{63}\text{.}5º$ south of east
Suppose a pilot flies $\text{40}\text{.}\text{0 km}$ in a direction $\text{60º}$ north of east and then flies $\text{30}\text{.}\text{0 km}$ in a direction $\text{15º}$ north of east as shown in [link] . Find her total distance $R$ from the starting point and the direction $\theta$ of the straight-line path to the final position. Discuss qualitatively how this flight would be altered by a wind from the north and how the effect of the wind would depend on both wind speed and the speed of the plane relative to the air mass.
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
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Got questions? Join the online conversation and get instant answers!
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2019-10-15 01:22:16
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https://www.physicsforums.com/threads/man-catching-a-bus.41643/
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# Homework Help: Man catching a bus
1. Sep 3, 2004
### CellCoree
A man is running at speed $$c$$ (much less than the speed of light) to catch a bus already at a stop. At $$t=0$$, when he is a distance $$b$$ from the door to the bus, the bus starts moving with the positive acceleration $$a$$.
Use a coordinate system with $$x=0$$ at the door of the stopped bus
i have two questions
What is $$x$$man$$(t)$$, the position of the man as a function of time? Answer symbolically in terms of the variables $$b$$, $$c$$ , and $$t$$ .
$$x$$man$$(t)$$ = _____________
(picture of the man and the bus is also included)
because the man's speed is constant, i used the formula
x(t) = x(0) + vt
so....
$$x$$man$$(t)$$ =0+ct
is that correct?
File size:
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884
2. Sep 3, 2004
### jamesrc
From the picture, it looks like the position of the man at time = 0 is x = -b. So the answer should be $$x_{\rm man}(t) = -b + ct$$
3. Sep 3, 2004
### CellCoree
i have another question
what is $$X$$bus$$(t)$$ the position of the bus as a function of time?
using the formula x(t) = x(0) +v(0)t + (1/2)at^2
x(t) = b +v(0)t +(1/2)ct^2
hmm what would be v(0)t? and is my setup correct? and what should i do next?
4. Sep 3, 2004
### jamesrc
That's the right formula, but think about what each variable means:
x(0) for the bus is 0, because the bus starts at x = 0.
v(0) for the bus is zero because it starts from rest
a for the bus is a (as stated in the problem)
so:
$$X_{\rm bus}(t) = \frac 1 2 at^2$$
5. Sep 4, 2004
### CellCoree
Inserting the formulas you found for $$x$$man$$(t)$$ and $$x$$bus$$(t)$$into the condition $$x$$man$$(t catch)$$ = $$x$$bus$$(t catch)$$, you obtain the following:
$$-b + ct$$catch$$=1/2at^2$$catch
Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man's speed $$c$$ so that the equation above gives a solution for $$t$$catch that is a real positive number.
Find $$c$$min, the minimum value of for which the man will catch the bus
how do i find $$c$$min?
6. Sep 4, 2004
7. Sep 6, 2004
### CellCoree
so your telling me to slove for cmin^2 -2ab =0 right?
so cmin = sqrt(2ab). is that the correct answer?
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2018-10-20 16:44:06
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https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/introduction-to-logarithmic-functions/
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## Introduction to Logarithmic Functions
### LEARNING OBJECTIVES
By the end of this lesson, you will be able to:
• Convert from logarithmic to exponential form.
• Convert from exponential to logarithmic form.
• Evaluate logarithms.
• Use common logarithms.
• Use natural logarithms.
In 2010, a major earthquake struck Haiti, destroying or damaging over 285,000 homes.[1] One year later, another, stronger earthquake devastated Honshu, Japan, destroying or damaging over 332,000 buildings,[2] like those shown in the picture above. Even though both caused substantial damage, the earthquake in 2011 was 100 times stronger than the earthquake in Haiti. How do we know? The magnitudes of earthquakes are measured on a scale known as the Richter Scale. The Haitian earthquake registered a 7.0 on the Richter Scale[3] whereas the Japanese earthquake registered a 9.0.[4]
The Richter Scale is a base-ten logarithmic scale. In other words, an earthquake of magnitude 8 is not twice as great as an earthquake of magnitude 4. It is ${10}^{8 - 4}={10}^{4}=10,000\\$ times as great! In this lesson, we will investigate the nature of the Richter Scale and the base-ten function upon which it depends.
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2019-09-16 20:30:25
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http://pdglive.lbl.gov/DataBlock.action?node=S032M&home=sumtabM
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${{\boldsymbol D}^{0}}$ MASS INSPIRE search
The fit includes ${{\mathit D}^{\pm}}$, ${{\mathit D}^{0}}$, ${{\mathit D}_{{s}}^{\pm}}$, ${{\mathit D}^{*\pm}}$, ${{\mathit D}^{*0}}$, ${{\mathit D}_{{s}}^{*\pm}}$, ${{\mathit D}_{{1}}{(2420)}^{0}}$, ${{\mathit D}_{{2}}^{*}{(2460)}^{0}}$, and ${{\mathit D}_{{s1}}{(2536)}^{\pm}}$ mass and mass difference measurements.
Given the recent addition of much more precise measurements, we have omitted all those masses published up through 1990. See any Review before 2015 for those earlier results.
VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT
$\bf{ 1864.83 \pm0.05}$ OUR FIT
$\bf{ 1864.84 \pm0.05}$ OUR AVERAGE
$1864.845$ $\pm0.025$ $\pm0.057$ 63k 1
2014
${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$1864.75$ $\pm0.15$ $\pm0.11$
2013 V
LHCB ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}$2 ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$
$1864.841$ $\pm0.048$ $\pm0.063$ 4.3k 2
2013 S
BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \Upsilon}{(4S)}}$
$1865.30$ $\pm0.33$ $\pm0.23$ 0.1k
2010 A
KEDR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at ${{\mathit \psi}{(3770)}}$
$1864.847$ $\pm0.150$ $\pm0.095$ 0.3k
2007
CLEO ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \phi}}$
1 Obtained by analyzing CLEO-c data but not authored by the CLEO Collaboration. The largest source of error in the TOMARADZE 2014 value is from the uncertainties in the ${{\mathit K}^{-}}$ and ${{\mathit K}_S^0}$ masses. The systematic error given above is the addition in quadrature of $\pm0.022 \pm0.053$ MeV, where the second error is from those mass uncertainties.
2 The largest source of error in the LEES 2013S value is from the uncertainty of the ${{\mathit K}^{+}}$ mass. The quoted systematic error is in fact $\pm0.043$ + 3 (${\mathit m}_{{{\mathit K}^{+}}}$ $−$ 493.677), in MeV.
References:
PR D89 031501 High Precision Measurement of the Masses of the ${{\mathit D}^{0}}$ and ${{\mathit K}_S^0}$ mesons
JHEP 1306 065 Precision Measurement of ${{\mathit D}}$ Meson Mass Differences
PR D88 071104 Measurement of the Mass of the ${{\mathit D}^{0}}$ Meson
PL B686 84 Measurement of ${{\mathit D}^{0}}$ and ${{\mathit D}^{+}}$ Meson Masses with the KEDR Detector
PRL 98 092002 Precision Determination of the ${{\mathit D}^{0}}$ Mass
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2020-02-27 06:01:46
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https://indico.cern.ch/event/356420/contributions/1764171/
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# EPS HEP 2015
22-29 July 2015
Europe/Vienna timezone
## Inner tracking devices at the Belle II experiment
Jul 24, 2015, 3:00 PM
15m
HS42
### HS42
talk Detector R&D and Data Handling
### Speaker
Giulia Casarosa (Sezione di Pisa (IT))
### Description
In the future Belle II experiment at the SuperKEKB collider in Tsukuba, Japan, charged particle tracking in the vicinity of the $e^+$ $e^-$ interaction point is provided by a two-layer silicon pixel detector based on the novel DEPFET technology (PXD) and by a four-layer silicon strip detector (SVD). In this presentation, we review the technology and the design of these two devices, and describe the current state of their construction.
Submitted on behalf of the Belle II collaboration. Actual presenter will be selected by the Belle II collaboration at a later time.
### Primary author
Christoph Schwanda (Austrian Academy of Sciences)
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2021-08-02 07:09:58
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https://www.wind-energ-sci.net/5/89/2020/wes-5-89-2020.html
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Journal topic
Wind Energ. Sci., 5, 89–104, 2020
https://doi.org/10.5194/wes-5-89-2020
Wind Energ. Sci., 5, 89–104, 2020
https://doi.org/10.5194/wes-5-89-2020
Research article 14 Jan 2020
Research article | 14 Jan 2020
# Hurricane eyewall winds and structural response of wind turbines
Hurricane eyewall winds and structural response of wind turbines
Amber Kapoor1, Slimane Ouakka2, Sanjay R. Arwade2, Julie K. Lundquist3,4, Matthew A. Lackner1, Andrew T. Myers5, Rochelle P. Worsnop6,7, and George H. Bryan8 Amber Kapoor et al.
• 1Mechanical & Industrial Engineering, University of Massachusetts Amherst, Amherst, MA 01003, USA
• 2Civil & Environmental Engineering, University of Massachusetts Amherst, Amherst, MA 01003, USA
• 3Atmospheric & Oceanic Sciences, University of Colorado Boulder, Boulder, CO 80309, USA
• 4National Renewable Energy Laboratory, Golden, CO 80401, USA
• 5Civil & Environmental Engineering, Northeastern University, Boston, MA 02115, USA
• 6University of Colorado, Cooperative Institute for Research in Environmental Sciences, Boulder, CO, USA
• 7NOAA/Earth System Research Laboratory, Physical Sciences Division, Boulder, CO 80305, USA
• 8National Center for Atmospheric Research, Boulder, CO 80305, USA
Abstract
This paper describes the analysis of a wind turbine and support structure subject to simulated hurricane wind fields. The hurricane wind fields, which result from a large eddy simulation of a hurricane, exhibit features such as very high gust factors (>1.7), rapid direction changes (30 in 30 s), and substantial veer. Wind fields including these features have not previously been used in an analysis of a wind turbine, and their effect on structural loads may be an important driver of enhanced design considerations. With a focus on blade root loads and tower base loads, the simulations show that these features of hurricane wind fields can lead to loads that are substantially in excess of those that would be predicted if wind fields with equally high mean wind speeds but without the associated direction change and veer were used in the analysis. This result, if further verified for a range of hurricane and tropical storm simulations, should provide an impetus for revisiting design standards.
1 Introduction
Activity related to offshore wind energy development continues to accelerate along the US East Coast. For example, the Massachusetts legislature recently proposed doubling the Massachusetts offshore wind energy commitment to 3200 MW (Massachusetts HR 2018), and a public price was tentatively set for the first 800 MW of offshore wind energy capacity in Massachusetts, an important step in the process of developing offshore wind farms. Awareness of potential hurricane risk to offshore wind farms along the US East Coast is high, and with potentially thousands of offshore wind turbines to be constructed over the coming decades, the quantification of this risk is crucial to ensure the safety, availability, and reliability of this important energy source.
Analytic models of hurricane wind fields (e.g., Holland, 1980; Holland et al., 2010), based on interpolations between sparse observations, have been useful for informing offshore wind design specifications (Tarp-Johansen and Clausen, 2006; Hallowell et al., 2018). However, these models cannot capture certain nonstationary features of hurricane eyewalls. Recent advances in observations (Stern et al., 2016; Wingo and Knupp, 2016; Wurman and Kosiba, 2018) and in hurricane simulation capabilities (Worsnop et al., 2017a; Wu et al., 2018) allow for the identification of sub-kilometer-scale features of hurricane wind fields, e.g., organized turbulent structures such as mesovortices, that may create significant and unforeseen loads on offshore wind turbines. Many of these characteristics are extremely difficult to measure during actual storms because they occur in or near the eyewall of the hurricane where wind speeds are extremely high and observations are difficult to make. Observation of the distribution and lifetime of these mesovortices may also require simultaneous measurement of wind speed and direction over spatial domains measured in the tens of kilometers.
The limited set of observations can be augmented through the use of large eddy simulations (LESs) that resolve these turbulent structures. LESs of hurricane wind fields can provide insight into organized structures within the hurricane eyewall, such as convective cells and transient large eddies. By using LESs, the energy-producing scales of three-dimensional atmospheric turbulence should be explicitly resolved, while finer scales of turbulence are parameterized by a subgrid-scale model. Reducing the grid size of an LES allows more of the three-dimensional turbulence to be resolved (i.e., computed directly) rather than parameterized through the subgrid-scale turbulence model. As a result, the maximum instantaneous wind speed in organized structures in the eyewall produced in these LESs tends to be highly sensitive to the resolution of the simulation (Rotunno et al., 2009).
The LES of Zhu (2008) investigated hurricane dynamics driven by realistic mesoscale weather forcing, with the finest horizontal resolution at 100 m in the innermost domain. This domain only comprised a small region of the inner core of the hurricane. The idealized simulations of Rotunno et al. (2009), at 62 m horizontal resolution, indicated very strong mesovortices with maximum instantaneous wind speeds of 120 m s−1. Green and Zhang (2015) explored how model resolution and the representation of the boundary layer affect the development of mesovortices and other fine-scale structures in the hurricane boundary layer, with some simulations as fine as 111 m horizontal resolution. They also suggest that the resolution of their simulations affected the size of the large eddy circulations, implying that finer resolution was required for convergence to a “true LES.” Worsnop et al. (2017a) simulated an idealized Category 5 hurricane with 32 m horizontal resolution using the Cloud Model I (CM1) of Bryan et al. (2016). Similar CM1 hurricane simulations with 62 m horizontal grid spacing were validated with observations of turbulence spectra by Worsnop et al. (2017b). Finally, the 37 m nested LESs of Wu et al. (2018) replicated tornadic structures within the eyewall of Typhoon Matsa.
Since industrial-scale offshore wind energy development along the US East Coast began to be discussed seriously, a series of studies have sought to quantify the degree of risk posed to offshore wind farms by hurricanes. These studies have included attempts to identify appropriate structural performance levels and nonlinear structural analysis methods for offshore wind structures (Wei et al., 2014, 2016), multihazard risk analyses (Hallowell et al., 2018; Kim and Manuel, 2016; Mardfekri and Gardoni, 2015; Valamanesh et al., 2015, 2016), and analysis of wind–structure interaction (Amirinia and Jung, 2017). On the whole, these studies have shown that hurricane winds can indeed pose important risks to offshore wind turbines but that such risk can be mitigated by appropriate design approaches. None of these studies, however, have incorporated the kind of high-resolution characterizations of hurricane wind fields that were described by Worsnop et al. (2017a). Therefore, while a substantial body of literature already exists related to the overall exposure of US East Coast offshore wind farms to hurricanes, this paper advances the state of knowledge by assessing the impact of specific and intense hurricane wind field characteristics that have not yet been considered.
Here, we analyze winds and turbulence from an LES of an idealized Category 5 hurricane using Cloud Model 1 (CM1), a three-dimensional, non-hydrostatic, nonlinear, time-dependent numerical model designed for idealized studies of atmospheric phenomena (Bryan and Rotunno, 2009a). These simulations have been used to identify wind field characteristics, such as gust factors, spatial coherence, velocity spectrum, shear profile, direction change, and veer (Worsnop et al., 2017a), that may be important drivers of offshore wind turbine response. We expand upon previous work by providing these wind characteristics to the wind field simulator TurbSim (Jonkman and Buhl Jr., 2009) and evaluating TurbSim's performance against LESs. TurbSim generates simulated wind fields representative of several of the characteristics identified in the LESs. Finally, the effects of this flow on a wind turbine are simulated using the DTU 10 MW reference wind turbine (Bak et al., 2013), which is a three-bladed, upwind, variable-speed turbine with a rotor diameter of 178 m and a 119 m hub height. This turbine is represented in FAST, a coupled aero–hydro–servo–elastic code developed by the National Renewable Energy Laboratory (Jonkman and Buhl Jr., 2005). Sim et al. (2012) used a similar procedure of defining FAST input by LESs to establish guidelines on the spatial and temporal resolution needed to ensure accurate estimates of wind turbine response to turbulent wind fields. Their simulations used the NREL 5 MW reference turbine and did not consider hurricane wind fields.
The Category 5 storm simulation used to develop the wind fields used in this paper is a severe storm, stronger than any likely to directly affect the US Atlantic coast from the Carolinas northward. Therefore, it is emphasized that the primary purpose of this paper is not to establish that a Category 5 hurricane imposes large loads on offshore wind structures, but rather that hurricanes contain wind field characteristics that are not currently considered in design and that may exacerbate loading in unexpected ways. In fact, it is unlikely that design codes should require resistance to a Category 5 storm since such a storm is so unlikely for most proposed wind energy areas.
The remainder of the paper is organized into three sections. First, the characteristics of the LES hurricane wind fields are described in Sect. 2. Next, the simulation of representative wind fields using TurbSim is described in Sect. 3. Finally, the results of the FAST analysis are introduced to quantify the effect of hurricane wind fields on blade and tower structural demands in Sect. 4.
2 Hurricane wind field characteristics
This section describes a statistical characterization and analysis of a large eddy simulation (LES) of an idealized Category 5 hurricane using Cloud Model 1 (CM1) (Bryan and Rotunno, 2009b), described in detail in Worsnop et al. (2017a). The characteristics of the simulated hurricane are based on Hurricane Felix, which made landfall in southern Mexico after traveling westward across the southern Caribbean in 2007. Although some of the characteristics of the hurricane were derived from Hurricane Felix, the results can be taken as representative of relatively small Category 5 storms. The outer simulation domain of 3000 km × 3000 km × 25 km includes the complete hurricane, including the eyewall and rainbands. To resolve turbulent motions in the eye and eyewall, an inner fine-mesh domain of 80 km × 80 km × 3 km uses horizontal grid spacing of 31.25 m and vertical grid spacing of 15.625 m. The model time step is 0.1875 s; 4 h after initialization, a steady state is achieved, and a subsequent 10 min of output is archived. For simplicity, the hurricane is specified to have zero translational velocity. In this paper, a subset of the complete simulation data is analyzed that covers a domain of 60 km × 60 km × 508 m using virtual towers with horizontal spacing of 1 km × 1 km. This domain encompasses the eyewall (the most intense part of the storm) and provides sufficient resolution to characterize the features of hurricane wind fields that are most likely to pose a danger to offshore wind energy installations.
The features of the LES wind field are analyzed in the rest of this section, with the goal of providing representative characterizations of the wind field for subsequent use in wind turbine simulations. The wind field statistics and features quantified over the 10 min reference period are wind speed time history statistics up to 4th order, 3 s gusts and gust factors, wind shear profile, 10 and 30 s wind direction change, and veer (change in the wind direction with respect to height). The remainder of the paper focuses on the effect of mean wind speed, veer, and direction change or misalignment on turbine loads. These characteristics have been selected from the richer set of parameters available from the LESs to most closely mimic, in the authors' experience, the parameters most often treated as primary in typical design-level analysis.
## 2.1 Overall wind speeds and selection of included grid points
The simulated hurricane includes the quiescent eye, the turbulent eyewalls, and the outer rainbands as seen in the averaged horizontal wind speed over the full 10 min simulation at the elevation (117.19 m) closest to the DTU turbine hub height of 119 m (Fig. 1). The eye of the hurricane, within which the wind speeds are low, extends to a radius R of approximately 10 km. The maximum mean wind speed of approximately 90 m s−1 occurs at a radius of approximately 12 km and then decreases as the distance from the eye increases. For subsequent analysis and input for turbine simulations, the LES wind fields are characterized at discrete radii from the hurricane center: 10 km (inner edge of the eyewall for this hurricane); 12 km (the radius of maximum mean wind speed for this hurricane); 15 km (approximate outer edge of the eyewall for this hurricane); and 20 km (well outside the eyewall for this hurricane).
Figure 1Mean horizontal wind speed near the DTU turbine hub height of 119 m for the entire 10 min simulation on a 1 km × 1 km grid. The four dashed circles represent the reference radii of 10, 12, 15, and 20 km.
For each discrete reference radius, multiple points in the LES domain are considered to increase the sample size for generating relevant statistics. Any grid point within ±100 m of a reference radius is considered to be associated with that radius (Fig. 2); a larger envelope could incorporate too large of a range of changing wind fields, especially within the eyewall. This approach yields 28 points at radii of 10 and 12 km, 20 points at 15 km, and 40 points at 20 km. Points of interest include the hub height and the bottom and top of the rotor disk or, more specifically, the grid point elevations closest to those elevations for the DTU turbine (117.19, 39.06, and 210.94 m, respectively).
Figure 2Virtual towers (black circles) in one quadrant of the LES domain horizontally spaced at 1 km resolution. Selected virtual towers are included in the analysis when they are within 100 m of the reference radii: 10 km (magenta), 12 km (red), 15 km (blue), and 20 km (orange). Reference radii are measured from the hurricane center.
## 2.2 Wind speed gusts
The 3 s gust is defined in the design requirements by the IEC (2009) as the peak 3 s average wind speed within a 10 min interval. Associated with the gust is the gust factor, defined as the ratio of the maximum 3 s gust to the local mean wind speed (IEC, 2009). The maximum gust considered by the IEC design requirements for a Class I turbine is 70 m s−1 with a 50 m s−1 mean wind speed at the hub height, corresponding to a gust factor of 1.4. During Typhoon Maemi in Japan, peak gusts of 74 m s−1 were measured when the mean wind speed was only 38 m s−1, corresponding to a gust factor of 1.95, much higher than that considered by the IEC (Ishihara et al., 2005). Typhoon Maemi caused significant damage to all the wind turbines in an onshore coastal wind farm, underscoring the importance of revisiting gust factor specifications. Similarly, two onshore wind farms in Puerto Rico (Santa Isabel and Punta Lima) were affected by hurricane Maria in 2017, a Category 4 hurricane at landfall. Santa Isabel missed the eyewall of the hurricane and survived relatively intact, while Punta Lima, which had a direct eyewall hit, experienced destructive damage (Gallucci, 2018; Kelley, 2017; Rocky Mountain Institute, 2017).
Gusts in the LESs exceed those considered by the IEC, which is expected since the simulated storm is Category 5 with mean wind speeds larger than those considered in the IEC design requirements. The maximum gust factor in the simulated hurricane, outside the quiescent zone within the eye, is approximately 1.7, substantially in excess of the IEC-recommended gust factor or 1.4. These results, along with a more detailed discussion of the wind speed and gust features of the simulated storm, are available in Worsnop et al. (2017a).
## 2.3 Change in wind direction and veer
Worsnop et al. (2017a) provide distributions of the 10 and 30 s maximum direction change at hub height at a range of radii from the storm center. At radii outside the quiescent zone, the mean maximum direction change ranges from approximately 15 to 20, and the maximum direction changes approach 35. To illustrate the character of the wind direction in time, Fig. 3 shows 10 min time series of the maximum direction change over periods of 10 and 30 s at radii of 10, 12, 15, and 20 km. The direction changes exhibit very rapid fluctuations, and the maximum values approach 30 for both the 10 and 30 s periods at 10 and 20 km radii. Rapid wind direction changes of that magnitude at such high wind speeds are likely to be difficult for even a functioning yaw control system to manage.
Figure 3Time series of maximum wind direction change at various radii (R) of the hurricane at hub height: (a) inner edge of eyewall R=10 km, (b) within eyewall R=12 km, (c) outer edge of eyewall R=15 km, and (d) outside the eyewall R=20 km. The red and blue lines represent the maximum wind direction change over moving intervals of 30 s (red) and 10 s (blue).
In addition to direction change over time at hub height, wind direction can also vary across a vertical profile at the same time instant. This vertical variation in direction, called veer, is next characterized for the simulated hurricane wind fields. Although numerous onshore observations of veer indicate its prevalence, especially at night, and veer associated with nocturnal low-level jets has been implicated in damage to onshore wind turbines (Kelley et al., 2006) and in affecting turbine power production (Vanderwende and Lundquist, 2012), veer is not currently considered in wind turbine design specifications, either onshore or offshore. Veer may cause additional demand on the blades since the rotor is only yawed and feathered relative to a single wind direction, usually sensed at the nacelle (Giebel and Gryning, 2004).
To characterize the veer quantitatively, four reference veer profiles are defined using the wind direction at the LES grid points closest to the hub height, rotor top, and rotor bottom elevations of the DTU reference wind turbine (117.19, 210.94, 39.06 m). The profiles (INC, DEC, VEE, INV) are defined according to the wind directions at the top of the rotor disk θtop, the hub height θhub, and the bottom of the rotor disk θbot, as shown in Table 1, and every instant of the simulation time histories is categorized into one of these profiles. Table 1 also shows the frequency of occurrence of each of the veer shapes and shows that INC, one of the monotonically varying veer profiles, dominates. Different veer profiles may induce different load conditions on the blades, rotor, and tower.
Table 1Percentage occurrence of the four different veer profiles at each reference radius.
Although the wind directions at the rotor top, hub height, and rotor bottom define the overall shape of the veer profile, the LESs provide the wind direction at a series of vertical points spaced at 15.625 m. The actual change in wind direction vertically across the rotor disk may be nonlinear (Fig. 4) as seen by the profiles with maximum veer within each profile type at each radius. The veer magnitude is defined as
$\begin{array}{}\text{(1)}& {\mathit{\theta }}_{\mathrm{veer}}=\left|{\mathit{\theta }}_{\mathrm{top}}-{\mathit{\theta }}_{\mathrm{hub}}\right|+\left|{\mathit{\theta }}_{\mathrm{hub}}-{\mathit{\theta }}_{\mathrm{bot}}\right|.\end{array}$
Direction changes of over 30 between the top and bottom of the rotor can occur within the hurricane boundary layer, particularly in the eyewall region.
Figure 4Maximum instantaneous veer profile for the four profile shapes at four radii from the hurricane center: (a) internal eyewall boundary R=10 km, (b) within eyewall R=12 km, (c) outer edge of eyewall R=15 km, and (d) outside the eyewall R=20 km. The hub height and rotor top and bottom of the DTU reference turbine, at elevations of 119, 208, and 30 m, respectively, are indicated with horizontal lines.
3 Generating hurricane wind fields in TurbSim
## 3.1 TurbSim inputs
To simulate a wind turbine in FAST subjected to hurricane wind conditions, TurbSimv2 is used to generate wind input files that are compatible with FAST and that capture the key characteristics of the wind fields produced by the LESs. TurbSim is a full-field, turbulent wind simulator developed by the National Renewable Energy Laboratory (Jonkman and Buhl Jr., 2005). Using statistics from the LES data at each of the four radii defined in Sect. 2, wind input files representing the wind field at each radius are generated. Each wind input file is 1 h long, consistent with IEC standards for wind turbine structural design and load calculations (IEC, 2009).
TurbSim requires inputs of mean reference wind speed and turbulence intensity at the turbine's hub height, spectrum (Kaimal in this case), wind shear profile, wind veer profile, and coherence exponent (applied to Eq. 18 in Jonkman and Buhl Jr., 2009). Given these parameters, TurbSim models turbulence as a Gaussian process with no skewness and kurtosis equal to 3, while the turbulence in the LES wind field can be non-Gaussian (see, e.g., Schoettler et al., 2017, for a further discussion of the impact of wind field non-Gaussianity).
## 3.2 TurbSim and LES data comparisons
The mean reference wind speed and turbulence intensity were determined using the LES data at a height nearest the hub height at z=117.19 m. Skewness and kurtosis are not TurbSim input parameters, and therefore comparison between the values of skewness and kurtosis indicate the goodness of fit of the marginal distribution of the TurbSim wind fields relative to those in the LESs.
Table 2Comparison of LES and TurbSim wind field statistics.
While the mean, turbulence intensity, and kurtosis of the two wind fields match almost exactly, the largest differences appear in the skewness (Table 2). (The mean and turbulence intensity should match since these two values are prescribed to TurbSim.) TurbSim assumes normally distributed turbulence statistics, and thus the skewness is nearly zero in all cases. The LES wind field has small but non-negligible skewness, resulting in large percentage differences between the two sets of wind files, though the absolute differences are small. Note that identical turbulence intensity has been applied to all three components of the wind field. To the authors' knowledge this is common practice in the design and analysis of offshore wind turbines. Further study of the possibility of turbulence intensity differences in the component wind directions would be a worthwhile contribution. Using the inputs as described, TurbSim did not replicate the gust factors observed in the LES data, with the TurbSim gust factors reaching a maximum of 1.3, significantly lower than observed in the LES data. Generating more intense gusts in TurbSim would require increasing the turbulence intensity or modifying the distribution of the wind speed, and such approaches should be developed in further work.
The wind shear profiles from LES and TurbSim are indistinguishable (Fig. 5). The wind shear profile for each radii was specified using the mean horizontal wind speed from LES for all grid cells between the top and bottom of the rotor disk. These shear profiles were then specified in TurbSim's User-Defined Profile, available in TurbSimv2. In both cases, the profile at the 10 km radius deviates from a standard power-law profile.
Figure 5Wind shear profile: the mean wind shear profile at R=10, 12, 15, and 20 km for both the LES and TurbSim wind field simulations. For reference, the three horizontal lines indicate the top and bottom of the rotor disk at 208 and 30 m, respectively, and the hub height at 119 m.
Two cases were considered for the wind veer profile: a baseline case with no veer and a case with veer. The veer profiles are specified in the TurbSim input file. In the “no-veer” case, the wind direction is 0 at all heights. In the veer case, at each radii, the four veer profiles shown in Fig. 4 are specified. As in the case of wind shear, the LES and TurbSim veer profiles match exactly and are thus not shown here. It should be noted that the veer profiles selected are worst-case instantaneous veer profiles from the 10 min simulation. Instantaneous veer profiles may overestimate the veer that drives structural response due to timescales associated with structural response to direction change. In the absence of consensus on how to average veer profiles to establish design veer profiles, the instantaneous worst case has been used here with the caveat that results may overestimate the impact of veer on structural response.
The power spectral density compares well between LES and TurbSim (Fig. 6). The hub height wind speed power spectral density created by TurbSim is modeled with a Kaimal spectrum. The temporal resolution of the LES data and the implicit subgrid-scale filter cause the power to fall off at high frequencies more quickly than the TurbSim data. Aside from this expected difference, the plots show a reasonable agreement between the two datasets at all four radii. While it is possible to specify a user-defined spectrum in TurbSim, the Kaimal spectrum was selected as a model to not make the simulations overly storm-specific, to mitigate the effects of temporal resolution in creating artifacts such as high-frequency roll-off in the spectra and to mimic what the authors understand to be standard practice in design and analysis. Furthermore, as with the turbulence intensities, transverse components of the wind field have been assumed to have the same spectral form.
Figure 6Power spectral density comparisons of the LES and TurbSim 10 min wind field simulations at hub height at four different radii from the hurricane center.
The coherence exponent controls the degree of spatial coherence between neighboring points as a function of distance between points (Jonkman and Buhl Jr., 2009). Coherence in the hurricane boundary layer may persist at larger horizontal separations than seen in non-hurricane boundary layers (Worsnop et al., 2017b). In TurbSim, the vertical coherence of the wind speed is defined for the x, y, and z components of wind individually by
$\begin{array}{}\text{(2)}& {\mathrm{Coh}}_{i,j}=\mathrm{exp}\left(-a{\left(\frac{r}{{z}_{\mathrm{m}}}\right)}^{\mathrm{CohExp}}\sqrt{{\left(\frac{fr}{{\stackrel{\mathrm{‾}}{u}}_{\mathrm{m}}}\right)}^{\mathrm{2}}+\left(br{\right)}^{\mathrm{2}}}\right),\end{array}$
where r is the vertical distance between points i and j, f is the cyclic frequency, CohExp is the coherence exponent input parameter, zm and ${\stackrel{\mathrm{‾}}{u}}_{\mathrm{m}}$ are the mean height and wind speed of points i and j, and a and b are the spatial coherence decrement and offset parameter for the component of the wind speed under consideration. The CohExp parameter provides primary control in the TurbSim input files and has been selected as the only coherence fitting parameter in the name of simplicity.
The appropriate value for the coherence exponent was evaluated by calculating the correlation coefficient between the hub height wind speed time series and the wind speed time series at all other heights in the LES data. Recall that the vertical spacing between grid points in the LES data is 15.6 m. The option for setting the coherence exponent value was limited by the TurbSim software. Through a process of trial and error, a single coherence exponent of 0.85 was selected for all locations for consistency between simulations, which is near the maximum allowable value of 1.0. This selection represents a significant increase in coherence compared to the default value of 0.0, but previous work indicates that the hurricane boundary layer likely contains coherent structures such as roll vortices that would increase the coherence of the flow (Worsnop et al., 2017b).
Figure 7Profiles of the correlation coefficient between the 10 min horizontal wind speed time series at each elevation and the 10 min horizontal wind speed time series at hub height for TurbSim (red) and LES (blue dashed) simulations at four different radii from the hurricane center.
As the coherence exponent increases, the correlation between the wind speed time series at spatially separated points also increases, increasing the variance of the total blade load and therefore the maximum load. The LES data tend to have higher spatial correlation in the vertical direction than the TurbSim data (Fig. 7). However, the default TurbSim coherence exponent of 0.0 causes poorer agreement as the vertical correlation within the TurbSim data drops off even more rapidly with distance than is seen in the LES data. Capturing the spatial coherence of the wind field to the greatest degree possible is important for estimating structural response because wind fields with longer-range coherence would be expected to generate greater variability in structural loads. This difference occurs because the blades act as lengthwise integrators of the local aerodynamic forces.
Table 3Wind field characteristics for the suite of simulation cases (n/a: not applicable).
4 Structural effects of hurricane winds on wind turbines
## 4.1 FAST simulations
Four cases were considered for each of the four radii: baseline hurricane winds (BASE), hurricane winds with veer (VEER), misaligned hurricane winds (MISAL), and, for comparison, winds at rated power (RATED). The BASE case represents an idling turbine with a wind field corresponding to the mean wind speed and turbulence intensity from the LES but without any veer or direction change. The VEER case considers the largest-magnitude veer case as described in Sect. 3 with the veer profile applied at 1 m vertical increments. The MISAL case considers the baseline wind with a yawed turbine to evaluate the impact of rapid direction change. The degree of yaw misalignment is determined for each location based on the maximum 10 s direction change described in Sect. 2. Yaw misalignment may occur if the wind changes direction more quickly than the yaw controller can adjust the nacelle. Since mean wind direction cannot vary temporally in FAST–TurbSim, yaw misalignment has been used as a surrogate for the effects of rapid direction change. For these three cases (BASE, VEER, and MISAL), the turbine blades are pitched to feather, the rotor is set to idle, and the generator is turned off. For the RATED case, an operational turbine is simulated. The rated wind speed case considers the turbine operating in conditions with a mean wind speed of 11.4 m s−1, a turbulence intensity of 10 %, power-law exponent of 0.1, and a coherence exponent of 0.0. The blade pitch and generator controllers are active during simulations, induction is disabled for idling cases, and aerodynamic loads on the tower are included. A 1 h simulation of the turbine response was performed for each wind field case. This record was then subdivided into six 10 min intervals, and the maximum turbine response was extracted for each 10 min interval. Table 3 summarizes the wind field characteristics for the full set of simulation cases, and the following tables provide the average of the six maximum responses of the 10 min simulation intervals. Subdividing a 1 h simulation into 10 min intervals introduces a minor correlation between the 10 min intervals, but since the timescales associated with turbulence are very small compared to the 10 min analysis interval, this effect is negligible. This procedure mitigates the need to allow transients to dissipate for each 10 min simulation and provides the ability to estimate variability across simulations.
## 4.2 Maximum turbine structural loads
When the BASE, VEER, or MISAL cases are applied to the turbine, the tower demands in the side-to-side (SS) direction and the blade demands in the rotor plane increase compared to the RATED case. The tower demands in the fore–aft (FA) direction and the blade demands out of the rotor plane are either reduced or do not increase significantly because the nonrated wind cases have the blades pitched to feather, reducing the impact of the wind in those directions. The MISAL wind causes the largest increase in loads, followed by VEER, then BASE. The increased loads due to wind misalignment and veer emphasize the importance of considering misalignment and veer when evaluating turbine structural response (Tables 4 through 8).
Table 4Maxima of blade and tower structural response to the BASE hurricane wind case. The scale factor (SF) indicates the magnitude of response relative to RATED. Numerical values of the scale factors are not provided when not appropriate (for blade deflections the blade is oriented differently in RATED, and the scaling of FA–SS tower base moment ratios is not a meaningful measure of response).
Table 5Maxima of blade and tower structural response to the VEER case. The scale factor (SF) indicates the magnitude of response relative to RATED. Cells highlighted in gray indicate values that exceed the Eurocode strength basis value for the tower (5.4×105 kNm) or the 18 m deflection limit on the blade tip. Numerical values of the scale factors are not provided when not appropriate (for blade deflections the blade is oriented differently in the rated case, and the scaling of FA SS tower base moment ratios is not a meaningful measure of response).
Table 6Maxima of blade and tower structural response to the VEER case. The scale factor (SF) indicates the magnitude of response relative to BASE. Cells highlighted in gray indicate values that exceed the Eurocode strength basis value for the tower (5.4×105 kNm) or the 18 m deflection limit on the blade tip. Numerical values of the scale factors are not provided when not appropriate (for blade deflections the blade is oriented differently in the rated case, and the scaling of FA SS tower base moment ratios is not a meaningful measure of response).
Table 7Maxima of blade and tower structural response to the MISAL case. The scale factor (SF) indicates the magnitude of response relative to RATED. Cells highlighted in gray indicate values that exceed the Eurocode strength basis value for the tower (5.4×105 kNm) or the 18 m deflection limit on the blade tip. Numerical values of the scale factors are not provided when not appropriate (for blade deflections the blade is oriented differently in the rated case, and the scaling of FA SS tower base moment ratios is not a meaningful measure of response).
Table 8Maxima of blade and tower structural response to MISAL case. Scale factor (SF) indicates magnitude of response relative to BASE. Cells highlighted in gray indicate values that exceed Eurocode strength basis value for the tower (5.4×105 kNm) or the 18 m deflection limit on the blade tip. Numerical values of scale factors are not provided when not appropriate (for blade deflections the blade is oriented differently in the rated case and scaling of FA SS tower base moment ratios is not a meaningful measure of response).
Hurricane wind field characteristics such as VEER and MISAL cause substantial increases in certain turbine (blade and tower) loads when compared to BASE and RATED cases (Tables 4 through 8). The BASE loads are presented as scale factors relative to the RATED loads in Table 4. The VEER loads appear as scale factors of RATED in Table 5 and scaled to BASE in Table 6. The MISAL loads appear as scale factors of RATED in Table 7 and scaled to BASE in Table 8.
The design of the DTU 10 MW turbine is specified by Bak et al. (2013). The base cross section of the tower is a hollow steel tube with a diameter of 8.3 m and a thickness of 38 mm. For a section with this geometry and with Imperfection Quality Class B, Eurocode (2007) (EN 1993 1–6) prescribes a flexural strength of 74 % of the yield moment. For the DTU 10 MW turbine tower, which is made with S355 steel with a yield stress of 355 MPa, the flexural strength of this section per Eurocode is 5.4×5 kNm. The 18 m blade deflection limit is a rounded limit based on the 18.3 m tower clearance in the DTU 10 MW turbine (Bak et al., 2013).
For selected loads, the BASE loads surpass those of the RATED case. While the BASE out-of-plane blade loads in Table 4 are less than the RATED loads, the in-plane values exceed what is expected of rated operation. Similarly, the side-to-side tower BASE moment increase is approximately 3 times greater than the fore–aft moment increase. However, the side-to-side moment for the RATED case is a factor of 10 lower than the fore–aft moment, so the resultant moment for the BASE cases is around 2 times the moment for RATED. The simulated storm is a Category 5, and therefore increased loads relative to RATED are expected.
The misaligned wind causes even greater load increases than the VEER case and does so for both the blades and the tower. Only the out-of-plane tip deflection is still lower than that of the RATED case. The in-plane tip deflection is around 20 times greater than the RATED in-plane tip deflection, reaching 50 m at a radial position of 12 km. This is a physically unrealistic tip deflection beyond the modeling and simulation capabilities of FAST–ElastoDyn as used in this study. The numerical magnitudes of the tip deflections should therefore not be taken as quantitatively meaningful, but rather as an indication that large blade deflections, of potential structural concern, are occurring during the loading. The side-to-side tower base moment also shows substantially higher results with, a moment 90 times greater than rated at a radial position of 10 km. When presented as a scale factor applied to the BASE case, the impact of potential yaw misalignment is particularly apparent with an increase on average for every load assessed. The resultant blade root bending moment is approximately 6 times that of the BASE case and 5 times greater than the RATED case, while the resultant tower base moment is approximately 2.5 times greater than the BASE case and 5.5 times greater than the RATED case.
Figure 8Time series of in-plane blade tip deflection for turbine simulations at a radial position of 12 km with rated wind (RATED), baseline wind (BASE), wind with veer (VEER), and misaligned wind (MISAL).
Figure 9Time series of the resultant moment at the blade root for turbine simulations at a radial position of 12 km with rated wind (RATED), baseline wind (BASE), wind with veer (VEER), and misaligned wind (MISAL).
Figure 10Time series of tower base resultant moment for turbine simulations at a radial position of 12 km with rated wind (RATED), baseline wind (BASE), wind with veer (VEER), and misaligned wind (MISAL).
## 4.3 Time series of select turbine structural loads at R=12 km
Time series provide an indication of how the load histories vary under the different wind cases with more detail than the maximum responses given in the preceding tables (Figs. 8–10). The 12 km radius, within the eyewall, has the highest mean wind speed and shows the greatest variation in loads as the wind changes. The misaligned flow (MISAL) causes the largest standard deviation and mean for in-plane tip deflection (purple line in Fig. 8), blade root resultant moment (purple line in Fig. 9), and tower base resultant moment (purple line in Fig. 10). The VEER case causes a greater mean than RATED for all three loads presented but a similar standard deviation for the tower base resultant moment. As presented above, the BASE wind (blue lines in Figs. 8–10) causes an increase in in-plane tip deflection and tower base resultant moment compared to RATED, but the mean and maximum blade root resultant moment decrease for BASE, while the standard deviation increases.
5 Conclusions
With the expansion of offshore wind off the US East Coast, critical questions emerge regarding hurricane-induced loads on offshore wind turbines. Given the paucity of high-rate observations of winds and turbulence offshore in turbine rotor altitudes, we have integrated atmospheric large eddy simulations (LESs) of an idealized Category 5 hurricane with the CM1 into the engineering wind field simulator TurbSim to estimate loads on a 10 MW turbine using FAST. In particular, we evaluate how turbine and tower structures respond to flows characteristic of the hurricane boundary layer, particularly the eyewall, such as high wind speeds, veer in wind profiles, and rapid wind direction changes.
TurbSim wind fields can represent the mean wind speed, turbulence intensity, power spectra, veer, coherence, and direction change (represented as yaw misalignment) as they were calculated in CM1's LES of a Category 5 hurricane. Significant veer across the rotor disk (approximately 30) and rapid direction changes at hub height (up to 30 in 10 s) occur in the LESs. Further, the hurricane boundary layer appears to impose a much stronger spatial coherence than is normally assumed, perhaps due to coherent structures in the eyewall. Simulations show that veer and direction change can dramatically increase loads on the blades and tower, in some cases by factors of 5 or more. In general, veer primarily increases blade loads, while rapid direction changes at hub height amplify both blade and tower loads. Hurricane loads on wind turbines may therefore exceed those loads predicted when hurricane wind fields are simulated without the inclusion of veer and rapid direction change. Yaw misalignment cases are specified in design standards such as IEC 61400-3, but for normal operating cases the magnitude of the misalignment is only 8 or 15 depending on the corresponding wind model. The results of this paper, however, show that much larger misalignments may occur due to rapid wind direction changes.
The loads calculated here should motivate further investigation into how the hurricane boundary layer affects wind turbines. This Category 5 storm, even though small in size compared to many Category 5 storms, represents an environmental scenario far more severe than could credibly affect the vast majority of wind energy areas. Simulations of weaker hurricanes, which would be more frequently expected, must assess more likely risks to large-scale deployments of wind turbines. Also needed are assessments of the likelihood of these conditions in order to dictate design conditions as part of a probabilistic design basis.
Refinements to the LES would also provide insight. The LESs are conducted assuming that the hurricane is over open ocean. The onshore version of the DTU 10 MW turbine is used along with these offshore wind fields to isolate the effect of hurricane wind field characteristics in the absence of other structural loading from waves. These LESs are not coupled with a wave model and therefore do not explicitly model wave effects. Without wind–wave coupling, such simulations cannot provide information regarding the sea state in the hurricane. Such coupling is needed to explore how the hurricane atmospheric and oceanic boundary layers would affect the entire turbine and support structures such as monopiles, jackets, and floating platforms and mooring systems. The work presented herein has demonstrated that the hurricane boundary layer can adversely affect offshore wind turbines and motivates subsequent examination with further refinements.
Data availability
Data availability.
Author contributions
Author contributions.
JKL, RPW, and GHB performed the LESs and data analysis as cited. AK, SO, SRA, MAL, and ATM performed the structural analysis of the wind turbine and generated the representative wind fields. All authors participated in preparing the paper.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Disclaimer
Disclaimer.
The views expressed in the article do not necessarily represent the views of the DOE or the US Government. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for US Government purposes.
Acknowledgements
Acknowledgements.
The authors acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by the National Center for Atmospheric Research's Computational and Information Systems Laboratory and sponsored by the National Science Foundation. This work was authored, in part, by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the US Department of Energy (DOE), and funding was provided by the US Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office.
Financial support
Financial support.
This research has been supported by the US National Science Foundation (grant nos. CMMI-1552559 and CMMI-1234656), the University of Bologna (grant prot. no. 1067 tit. III cl.12), and the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the US Department of Energy (DOE; contract no. DE-AC36-08GO28308).
Review statement
Review statement.
This paper was edited by Johan Meyers and reviewed by two anonymous referees.
References
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Holland, G. J., Belanger, J. I., and Fritz, A.: A Revised Model for Radial Profiles of Hurricane Winds, Mon. Weather Rev., 138, 4393–4401, https://doi.org/10.1175/2010MWR3317.1, 2010.
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Ishihara, T., Yamaguchi, A., Takahara, K., and Matsuura, S.: An Analysis of Damaged Wind Turbines by Typhoon Maemi in 2003, 6th Asian Pacific Conference on Wind Engineering, Seoul, South Korea, 1413–1428, 2005.
Jonkman, J. B. and Buhl Jr., M.: TurbSim user's guide, NREL, Golden, CO USA, 2009.
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Kapoor, A.: LES wind files and offshore turbine response files for Category 5 hurricane, available at: https://github.com/alkapoor/Hurricane-LES-and-Turbine-data, last access: 8 January 2020.
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2020-02-26 11:27:24
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https://ftp.aimsciences.org/article/doi/10.3934/dcds.2013.33.2523
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Article Contents
Article Contents
# Ergodicity of certain cocycles over certain interval exchanges
• We show that for odd-valued piecewise-constant skew products over a certain two parameter family of interval exchanges, the skew product is ergodic for a full-measure choice of parameters.
Mathematics Subject Classification: Primary: 37A20, 37E10, 37A25; Secondary: 37E35.
Citation:
• [1] J. Chaika and P. Hubert, Ergodicity of skew products over interval exchange transformations, in preparation. [2] J.-P. Conze, Recurrence, ergodicity and invariant measures for cocycles over a rotation, in "Ergodic Theory" Contemp. Math. AMS, 485 (2009), 45-70.doi: 10.1090/conm/485/09492. [3] J.-P. Conze and K. Frączek, Cocycles over interval exchange transformations and multivalued Hamiltonian flows, Advances in Mathematics, 226 (2011), 4373-4428. [4] S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials, Annals of Mathematics, 124 (1986), 293-311. [5] A. Ya. Khinchin and A. Ya., "Continued Fractions," Dover Publications Inc., Mineola, NY, 1997. [6] L. Kuipers and H. Niederreiter, "Uniform Distribution of Sequences," Wiley-Interscience, New York, 1974. [7] K. Schmidt, "Cocycles on Ergodic Transformation Groups," Macmillan Lectures in Mathematics, 1, Delhi 1977.
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2023-03-24 19:34:55
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http://demonstrations.wolfram.com/ElectrostaticBondingForcesBetweenAtoms/
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# Electrostatic Bonding Forces between Atoms
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.
Requires a Wolfram Notebook System
Edit on desktop, mobile and cloud with any Wolfram Language product.
This Demonstration examines bonding forces by placing a charge between two separated ions. The contour represents the curve where the repulsive and attractive forces are counterbalanced by the charge. Changing the charge ratio lets you examine heteronuclear () to ionic () species.
Contributed by: Eric R. Bittner,Department of Chemistry, University of Houston (March 2011)
Open content licensed under CC BY-NC-SA
## Details
Theoretical Details:
This Demonstration examines the electronic bonding forces between two ions A and B separated by a distance along the axis. In the absence of any electrons, the repulsive force between the ions acting along the A-B axis would be
.
Now, suppose we put a single charge, , at some point P in the - plane. We then have two attractive forces and between the ions and the point charge. If we consider the component of along the A-B bond axis, we can define a bonding force,
,
where and denote the angles PAB and PBA, respectively. In a molecule, the bonding force is then computed by taking the expectation value over the electronic state ; however, we can gain some insight into bonding by simply looking at the functional form of . For this we follow the discussion in Barry, Rice, and Ross [1] that in turn is based upon ideas introduced by Kajans and Berlin [2]. This is also discussed in the classic book by Hirschfelder, Curtiss, and Bird [3].
First, whenever the charge is located between the two ions, there is an attractive force, since and , hence . Likewise, if any charge is placed "behind" either ion, there is a destabilizing force, since . The curve where is then the demarcation between the bonding and anti-bonding regions.
The boundary surface given by
,
where and depends on only one physical parameter, the charge ratio between the two ions. By varying this parameter you can see how bonding occurs between different ionic species. corresponds to any homonuclear diatomic species, while various heteronuclear species correspond to . For example, corresponds to NaCl and corresponds to HCl.
References [1] R. S. Berry, S. A. Rice, and J. Ross, Physical Chemistry, New York: Wiley, 1980. [2] K. Fajans and T. Berlin, "Quantization of Molecules, Inter- and Intramolecular Forces," Phys. Rev. 63(7-8), 1943 pp. 309–312. [3] J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, New York: Wiley, 1954.
## Permanent Citation
Eric R. Bittner,Department of Chemistry, University of Houston
Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send
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2019-04-26 02:40:14
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http://benholmes.co.uk/posts/2017/11/logarithmic-potentiometer-laws
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# Modelling logarithmic potentiometer laws
Published:
This post presents a general logarithmic potentiometer law with a curve fit to enable a user to choose a curve that sounds good in their application. The law is computationally expensive as it involves an exponent but is good in terms of flexibility.
## Background
Recently I have been looking at circuits with potentiometers. They are everywhere in synthesisers, guitar pedals, etc. and used for controlling aspects of circuit behaviour by changing two resistances between three points.
Potentiometers (pots for short) come in a few flavours: linear, logarithmic, and anti-log. This name defines how the resistance changes with respect to the position of the wiper along the track of the pot. A linear pot means that the primary resistance is proportional to the wiper position, while the secondary resistance is the remaining resistance.
In this formulation, $0 \leq \alpha \leq 1$.
Whereas a linear potentiometer can be seen as straight, the remaining potentiometer laws are curvy. A curved mapping is useful for when controlling things such as volume, where our perception fits closely to a curve. The definition of the exact curve of a potentiometer is difficult to pin down as they differ with manufacturer and also price. For use in simulation, we can define a set of curves that a user can choose from for their needs.
## Logarithmic general form
The general form of the curve is given by
where $x$ is the wiper position, $y$ is the primary resistance, and $a$, $b$ and $c$ are free parameters for curve fitting.
This mapping is applied prior to calculating resistances, so will effectively map $x$ to $\alpha$, i.e. $y=\alpha$. For this reason it can be assumed that the limits of both $x$ and $y$ are zero and one. To fit this curve we then have two equations, when both $x$ and $y$ are 0:
And therefore we are given a simpler equation with only two parameters:
Constraining with our second set of points:
There is still one equation left to determine the parameter values. I find it useful to map this as a mid-point of the curve, for example saying that when the wiper is at half way I want the resistance to be at 10% of the total. This can be parameterised again so that we can change the midpoint, saying $x = 0.5$, $y = y_m$. This gives our final constraint
## Results
By setting the value for $y_m$ we can create a variety of mappings:
Note that when setting $y_m = 0.5$ that $b = \infty$! But for this value we can just use a linear map so no need to waste the computation time for the exponent.
Choosing for example $y_m = 0.15$ will give quite a good approximation of a log pot, though I say this without measurements or further evidence. For an anti-log pot one could select a value around $0.85$.
If you’re interested in further playing around with this, here is the MATLAB gist (although it should be fairly compatible to Octave, and also self-explanatory if you want to port it):
Tags:
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2018-11-16 07:34:56
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https://jp.mathworks.com/help/fininst/floorbybk.html
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# floorbybk
Price floor instrument from Black-Karasinski interest-rate tree
## Syntax
``````[Price,PriceTree] = floorbybk(BKTree,Strike,Settle,Maturity)``````
``````[Price,PriceTree] = floorbybk(___,Reset,Basis,Principal,Options)``````
## Description
example
``````[Price,PriceTree] = floorbybk(BKTree,Strike,Settle,Maturity)``` computes the price of a floor instrument from a Black-Karasinski interest-rate tree. `floorbybk` computes prices of vanilla floors and amortizing floors.```
example
``````[Price,PriceTree] = floorbybk(___,Reset,Basis,Principal,Options)``` adds optional arguments.```
## Examples
collapse all
Load the file `deriv.mat`, which provides `BKTree`. The `BKTree` structure contains the time and interest rate information needed to price the floor instrument.
`load deriv.mat;`
Set the required values. Other arguments will use defaults.
```Strike = 0.03; Settle = '01-Jan-2004'; Maturity = '01-Jan-2007';```
Use `floorbybk` to compute the price of the floor instrument.
`Price = floorbybk(BKTree, Strike, Settle, Maturity)`
```Price = 0.2061 ```
Load `deriv.mat` to specify the `BKTree` and then define the floor instrument.
```load deriv.mat; Settle = '01-Jan-2004'; Maturity = '01-Jan-2008'; Strike = 0.045; Reset = 1; Principal ={{'01-Jan-2005' 100;'01-Jan-2006' 60;'01-Jan-2007' 30;'01-Jan-2008' 30};... 100};```
Price the amortizing and vanilla floors.
```Basis = 1; Price = floorbybk(BKTree, Strike, Settle, Maturity, Reset, Basis, Principal)```
```Price = 2×1 2.2000 2.5564 ```
## Input Arguments
collapse all
Interest-rate tree structure, specified by using `bktree`.
Data Types: `struct`
Rate at which cap is exercised, specified as a `NINST`-by-`1` vector of decimal values.
Data Types: `double`
Settlement date for the floor, specified as a `NINST`-by-`1` vector of serial date numbers or date character vectors. The `Settle` date for every floor is set to the `ValuationDate` of the BK tree. The floor argument `Settle` is ignored.
Data Types: `double` | `char` | `cell`
Maturity date for the floor, specified as a `NINST`-by-`1` vector of serial date numbers or date character vectors.
Data Types: `double` | `char` | `cell`
(Optional) Reset frequency payment per year, specified as a `NINST`-by-`1` vector.
Data Types: `double`
(Optional) Day-count basis representing the basis used when annualizing the input forward rate, specified as a `NINST`-by-`1` vector of integers.
• 0 = actual/actual
• 1 = 30/360 (SIA)
• 2 = actual/360
• 3 = actual/365
• 4 = 30/360 (PSA)
• 5 = 30/360 (ISDA)
• 6 = 30/360 (European)
• 7 = actual/365 (Japanese)
• 8 = actual/actual (ICMA)
• 9 = actual/360 (ICMA)
• 10 = actual/365 (ICMA)
• 11 = 30/360E (ICMA)
• 12 = actual/365 (ISDA)
• 13 = BUS/252
Data Types: `double`
(Optional) Notional principal amount, specified as a `NINST`-by-`1` of notional principal amounts, or a `NINST`-by-`1` cell array, where each element is a `NumDates`-by-`2` cell array where the first column is dates and the second column is associated principal amount. The date indicates the last day that the principal value is valid.
Use `Principal` to pass a schedule to compute the price for an amortizing floor.
Data Types: `double` | `cell`
(Optional) Derivatives pricing options structure, specified using `derivset`.
Data Types: `struct`
## Output Arguments
collapse all
Expected price of the floor at time 0, returned as a `NINST`-by-`1` vector.
Tree structure with values of the floor at each node, returned as a MATLAB® structure of trees containing vectors of instrument prices and a vector of observation times for each node:
• `PriceTree.PTree` contains floor prices.
• `PriceTree.tObs` contains the observation times.
• `PriceTree.Connect` contains the connectivity vectors. Each element in the cell array describes how nodes in that level connect to the next. For a given tree level, there are `NumNodes` elements in the vector, and they contain the index of the node at the next level that the middle branch connects to. Subtracting 1 from that value indicates where the up-branch connects to, and adding 1 indicated where the down branch connects to.
• `PriceTree.Probs` contains the probability arrays. Each element of the cell array contains the up, middle, and down transition probabilities for each node of the level.
collapse all
### Floor
A floor is a contract that includes a guarantee setting the minimum interest rate to be received by the holder, based on an otherwise floating interest rate.
The payoff for a floor is:
$\mathrm{max}\left(FloorRate-CurrentRate,0\right)$
## Version History
Introduced before R2006a
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2022-05-24 00:17:19
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https://blog.csdn.net/cumian9828/article/details/108158995
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# 使vim变正常_我为什么爱Vim：鲜为人知的功能使其变得如此惊人
by Amit Kulkarni
Since I started using Vim in 2016, I’ve discovered several lesser-known features that Vim offers out of the box without any plugins.
#### 在开始涉猎这些新事物之前，您能否涵盖一些基础知识？ (Can you cover some basics before you start rambling about these new things?)
Oh sure! Before I copy paste a few commands from a cheatsheet, I am going to make a bold assumption: you wouldn’t be reading this if you wanted a cheatsheet and you already knew Vim basics.
You might have just heard that Linux distributions ship with a default command-line text editor called Vim, and may want to just give it a try.
So, let’s assume you are completely new to this whole game and start from just what we need as basics (without history/boring theory).
NOTE: If you know the basics, click here to scroll past them
Most of intro articles on Vim begin with modes of Vim, inserting, saving and exit. If you’re really in the mood of theoretical perfection learning mode, feel free to read whatever helps in wikibooks.
There are also some great books and articles that tell you that there is a philosophy behind the way Vim works and that the commands in VI/Vim are meant to be combined. Absolutely true and I’m sure you will appreciate it once you get used to the editor and the power it provides.
#### 我听过有趣的故事，并看到了有关Vim学习曲线的有趣图像。 真的吗？ 真的那么糟糕吗？ (I have heard funny stories and seen funny images about learning curve of Vim. Is that true? Is it actually that bad?)
Well, haters gonna hate ? However, according to me, the image that somewhat gives a proper representation of Vim is:
The majority of the articles on Vim refer to the learning *curve* as a learning *wall*, but hey, there’s some positivity: look at the other side of the wall!
Vim上的大多数文章都将学习*曲线*称为学习*墙*，但是嘿，有一些积极性：看看墙的另一面！
For beginners, it’s literally a wall since they have never done anything like this before to use an editor on command line. The thing that appealed most to me when I started as a beginner was the ubiquity of Vim.
Log in to any (non-windows) machine from any terminal and you can literally get an editor by typing *vi* with your eyes closed. The editor will appear in front of you!
Another thing that appealed to me is the ability to work without a mouse and without wasting any productive time on touchpad or getting a mouse for laptop.
I know, I know, I can hear some of you yelling “Emacs! Emacs!” I get it. But once I was hooked to Vim, I just never really had any interest in emacs (may be because of the installation required). So, yeah emacs is also great I guess. Feel free to jump ship before you start sailing on this beautiful journey with VI(m).
#### 我刚打开终端，输入vi并按回车键。 我所看到的只是一个欢迎屏幕。 我无法输入，也不知道该如何摆脱。 您确定它是功能强大的编辑器吗？ (I just opened my terminal and typed vi and hit return key. All i see is a welcome screen. I can’t type and I don’t know how to get out of it. Are you sure it’s a powerful editor with capabilities?)
100% sure. The behavior you just witnessed is the *wall* we saw earlier. Trust me VI(m) can do a lot of other things. It just has its own ways of using it. You can edit files, open tabs, split screen horizontally or vertically, browse file system, run linux commands without leaving your file, trigger make builds from your source code without exiting the file, bookmark directories, even better: bookmark lines of a file, find and replace words, of course copy-paste and a lot more.
100％肯定。 您刚刚看到的行为是我们之前看到的* wall *。 相信我，VI(m)还能做很多其他事情。 它只是有自己的使用方式。 您可以编辑文件，打开标签页，水平或垂直拆分屏幕，浏览文件系统，在不离开文件的情况下运行linux命令，在不退出文件的情况下触发源代码进行的构建，书签目录，甚至更好：文件的书签行，查找和替换单词，当然还有复制粘贴等等。
#### 是的 这样，对于编辑人员而言，支持这些工作意义重大。 Me！ 每个人都这样做。 有什么大不了的？ (Yeah! Like that’s a big deal for an editor to support those. Meh! Everyone does that. What’s the big deal?)
There’s no big deal, the only deal I see is the ability to focus on your file/code without leaving keyboard. Really, if you don’t mind using a mouse, then go ahead and open your MS word/GUI Editor and do all the editing you wish to do.
#### 很公平。 但是，认真地为什么不为某些工作使用IDE？ (Fair enough. But, seriously why not an IDE for some work?)
Okay, so you are a developer and have had some liking/love for an IDE. No, VI(m) is not a replacement for your shiny IDE. VI(m) does not have the out of the box awesome capabilities of your IDE. VI(m) is just small in size (package and installation) compared to the bulky IDEs and is available to use without any configuration and installations. Seriously, VI(m) is no match for some great things your IDE provides.
#### 聊够了，告诉我基础知识吗？ (Enough talk, show me the basics?)
Sure, before you begin, just keep in mind that any Vim user has to basically deal with command mode and insert mode. There’s no escape (literally, not the Esc key).
Let’s say you are using some editor and you want to delete a long function in C language. The simple steps you do are: Position your cursor at the beginning of the line, then press Shift + Down arrow till end or use mouse. This action that you had to do to select those lines required you to *stop* typing and press keys. Isn’t it? Don’t tell me you were typing something and simultaneously pressed keys to magically select the body of your function.
Be reasonable. You paused typing and did the selection work to tell your editor that you want to do something with this text (copy/cut/Bold/italics/anything).
This pause that you took is equivalent to being in command mode in VI(m). This is the time when you tell VI(m) that you want to do some actions on some lines/word/anything and you are not going to type. Now, VI(m) throws you out of insert mode and you are locked out of typing text in your file. Obviously, the other mode in which you can actually type in your file is the insert mode.
BTW, if you were wondering how are you selecting body of function without selecting text or using mouse, I accomplish that by placing the cursor on the opening braces and using keystrokes: d%
Yes, that deletes the contents of your function body. No, that’s not some creepy combination of keys to remember! d indicates you want to delete something. % is going to move the cursor to the end of the matching brace.
Now, that we have established the basic modes, let’s dive into basic VI(m).
If you know the name of the file you are writing:
$vi myfile.c If you are not sure of file name and want to start typing: 如果不确定文件名并要开始输入： $ vi
As soon as you open vi, you will be in the command mode. To enter insert mode, press i . Type whatever you wish. Press Esc to return to command mode. Now you have a few options to exit depending on how you opened vi.
If you gave a file name: :w will write those changes safely to disk. :q will quit the editor. You can combine these actions with : :wq and Return key
If you did not give a filename: :wq filename.c will write the contents to the file filename.c and quit the editor. If you are not interested in the text you wrote and wish to exit without saving anything: :q! and you are out! The ! is required at the end to say : “Yes, I am sure I don’t want to save the contents and I want to get out urgently”
There you go! You just created, edited and saved(or may be not) your first vi file. Congratulations ?
As I mentioned earlier, this is not a beginner’s introduction to VI(m). There are plenty of other articles (I will provide reference at the end of article) to get started. I just inserted that intro so that you’re not disappointed after landing on this page and finding nothing to learn?
This is the line where beginners say goodbye to intermediate users and head to the reference section for more brilliant intro articles.
Welcome to the intermediate users. These are some cool capabilities of VI(m) that I wasn’t aware of. But now I use them daily to be more productive.
For those of you who prefer TL;DR:
• tab-pages
标签页
• sessions
会议
• line numbers (+ marks) and copy/paste
行号(+号)和复制/粘贴
• folds
褶皱
• indention with =
缩进=
• insert-completion
插入完成
• netrw
网络
• splits/windows
拆分/窗口
• :! and a little bit about :make
:! 还有一点关于:make
#### 您是否提到了Vim中的标签？ 我不知道那个存在！ (Did you mention tabs in Vim? I didn’t know that existed!)
I know, right! A tab page is a page with one or more windows with a label (aka tab) at the top.
If you are interested in knowing more about windows, buffers, tab pages: technical details
Have a look:
Steps:
• Open Vim with any file or just Vim: $vim file1 用任何文件或仅用Vim打开Vim： $ vim file1
• Type the contents of file and get into command mode (Press Esc )
输入文件内容并进入命令模式(按Esc )
• :tabedit file2 , will open a new tab and take you to edit file2
:tabedit file2 ，将打开一个新选项卡，并带您编辑file2
• :tabedit file3 , will open a new tab and take you to edit file3
:tabedit file3 ，将打开一个新选项卡，并带您编辑file3
• To navigate between these tabs, you can be in normal mode and type : gt or gT to go to next tab or previous tab respectively. You can also navigate to a particular index tab (indexed from 1) using {i}gt where, i is the index of your tab. Example: 2gt takes you to 2nd tab
要在这些选项卡之间导航，您可以进入普通模式并键入： gtgT分别转到下一个选项卡或上一个选项卡。 您还可以使用{i}gt导航到特定的索引标签(从1开始索引)，其中i是标签的索引。 示例： 2gt带您进入第二个选项卡
• To directly move to first tab or last tab, you can enter the following in command mode: :tabfirst or :tablast for first or last tab respectively. To move back and forth : :tabn for next tab and :tabp for previous tab
要直接移至第一个选项卡或最后一个选项卡，可以在命令模式下输入以下内容:tabfirst:tablast分别用于第一个或最后一个选项卡。 来回移动:tabn用于下一个选项卡， :tabp用于上一个选项卡
• You can list all the open tabs using : :tabs
您可以使用:tabs列出所有打开的:tabs
• To open multiple files in tabs: $vim -p source.c source.h 要在选项卡中打开多个文件： $ vim -p source.c source.h
• To close a single tab: :tabclose and to close all other tabs except the current one: :tabonly . Use the suffix! to override changes of unsaved files
要关闭一个标签：： :tabclose并关闭除当前一个标签之外的所有其他标签:tabonly 。 使用后缀! 覆盖未保存文件的更改
I think this feature enables us to effectively save time by sharing the buffer between tabs and enabling us to copy paste between tabs and keep multiple sessions of different tab set for category of work. Example: You can have a terminal tab with all Vim tabs of source code C files only and you can have another terminal tab with all Vim tabs of header files (.h).
#### 标签提供了很多便利，可以使我的所有文件保持打开状态并在需要时访问它们。 但是，每次重新启动或关闭并打开终端时打开所有选项卡是否很痛苦？ (Tabs provide so much convenience to keep all my files open and access them when I want. However, isn’t it a pain to open all tabs every time I reboot or close and open the terminal?)
Right! We all like to have our own sessions of work in which we work with a set of files and would like Vim to restore that session of tabs the way we left it.Vim allows us to save and restore those tab sessions! ✋
Steps:
• Open any number of tabs you wish to work with
打开您希望使用的任意数量的标签页
• From any tab, press Esc and enter the command mode
在任何选项卡中，按Esc并进入命令模式
• Type :mksession header-files-work.vim and hit enter
输入:mksession header-files-work.vim并按回车
• Your current session of open tabs will be stored in a file header-files-work.vim
当前打开的选项卡会话将存储在文件header-files-work.vim
• To see restore in action, close all tabs and Vim
要查看实际还原，请关闭所有标签和Vim
• Either start vim with your session using : $vim -S header-files-work.vim or open vim with any other file and enter command mode to type: :source header-files-work.vim and BOOM! All your tabs are opened for you just the way you saved it! 使用以下命令在您的会话中启动vim： $ vim -S header-files-work.vim或使用任何其他文件打开vim并进入命令模式键入:source header-files-work.vim和BOOM！ 保存方式将为您打开所有标签！
• If you change any session tabs (close/open new), you can save that back using : :mks! while you are in the session
如果更改任何会话选项卡(关闭/打开新的)，则可以使用:mks!将其保存回来:mks! 在会议中
#### 是否可以在不知道行号的情况下复制/剪切粘贴？ (Can I copy/cut paste without having to know line numbers?)
Oh Yes! Earlier I used to see the line numbers ( :set nu ) of the functions I wanted to copy/cut. Let’s say I want to copy/cut lines 34 to 65. I used :34,65y (Copy/Yank) or :34,65d (Cut/Delete).
Of course counting the lines and using {n}yy or {n}dd (where n is number of lines) is not an option for hundreds of lines ?
There can be some functions that span multiple pages and you don’t want to go down only to forget what was the first line number. There’s a simple way to achieve this without worrying anything about line numbers!
Steps:
• Enter normal mode, go to the start line
进入普通模式，转到开始行
• Type mk (Mark point with alphabet ‘k’ or use any other alphabet)
键入mk (用字母“ k”标记点或使用其他任何字母)
• Move down (page down or whatever) and move to the end line
向下移动(向下翻页或其他操作)并移至结束行
• y'k will yank/copy all the lines from start to end
y'kÿANK /复制所有从开始到结束的线条
• d'k will cut/delete all the lines from start to end
d'k将剪切/ d从头到尾删除所有行
#### 我的文件顶部有一些烦人的长函数，我不想浪费时间滚动或跳转到行。 这可能要问很多，因为这不是IDE，但是，我们有机会折叠代码块吗？ (I have some annoying long functions at the top of my file and I don’t want to waste my time scrolling or jumping to lines. This may be a lot to ask because this is not an IDE but, by any chance can we fold the code blocks?)
Absolutely! Let’s say you want to skip remembering those line numbers and walk around with your new found love *the markers*. Go to the beginning of the function body and type mb . Now, just go to the end of the function body using % (brace matching) or any other convenient technique and press zf'b and you’re done!
Before and after:
If you are comfortable using the line numbers, the command is even easier to remember: :5,16fo (fo stands for code fold). Once you have folded your code, it’s easy to toggle between open and closed views using zo (Open the code fold) and zc (Close the code fold). Don’t stress it so much. Just use za to toggle between open and closed folds ?
Let’s say you spent considerable time folding your functions in a large file, you would obviously want to retain those folds every time you open that file right? (If not, why did you waste your energy folding them!?), so there’s a solution right in your ~/.vimrc . Insert the following lines in ~/.vimrcand your code folds are saved and restored:
autocmd BufWinLeave *.* mkview
autocmd BufWinEnter *.* silent loadview
#### 我通常会缩进，但有时我不得不编辑其他白痴的源代码，这使我无法编辑没有缩进的他/她的代码。 是否有任何神奇的按键操作可以做到这一点？ (I’m usually careful with my indentation but sometimes, I have to edit some other idiot’s source code and it bugs me to edit his/her code without indentation. Are there any magical keystrokes to make that happen?)
Sure! It’s as simple as: =i{ . Really that’s all ! ( i is inner object)
Before-after:
All you have to do is place the cursor anywhere within a block you want to indent, press Esc to enter normal mode and then: =i{ . Boom! Your entire function body (including inner blocks) is indented.
NOTE: Don’t expect indentation of your python files ?. It only works when Vim can identify the start and end using opening and closing parenthesis)
You can also increase/decrease the indentation within a block using : >;i{ to increase and <i{ to decrease in normal mode.
#### 我可能在做梦，但是(*颤抖的声音*)，我的意思是我只想尝试一下，嗯，我可能会为此而努力，但是(* 5秒暂停*)..没关系，让步关于我的下一个问题 (I may be dreaming but (*quavering voice*), I mean I just want to give it a try, Uhmm, I may be pushing it really far with this one but (*5 second pause*)..never mind, lets move on to my next question)
Vim is quite open-minded to take criticism or face the fact that it’s not an IDE, go ahead, let’s see what you’ve got.
Vim态度开放，可以接受批评或面对它不是IDE的事实，请继续，让我们看看您所拥有的。
#### 嗯，对不起，但是无论如何(*喘气*)任何插件或东西，vim会像IDE一样自动完成吗？ (Uhmmm, sorry but by any chance (*panting*) with any plugin or something, does vim have autocomplete like an IDE?)
? You may be surprised but yes it does! ? and guess what…* drum rolls ** drum rolls ** drum rolls ** drum rolls *
？ 您可能会感到惊讶，但是可以！ ？ 猜猜是什么... *鼓卷**鼓卷**鼓卷**鼓卷*
Without a plugin!
You heard me right! The only condition for Vim to show you options is “Vim should know what you’re talking about.” It could be through an included source file or defined functions or variables.
All you have to do is start typing and then press Ctrl+n in insert mode.
Just imagine the uses! Specially if you’re writing C code and you cannot recollect the exact OpenSSL library call, all you have to do is include the header!
Let me remind again: No plugins required ?
NOTE: The header files may be at some other locations on Mac and Vim may not be able to find them. I just use a Mac to login to a linux machine. So, if you’re using Mac, sorry about that.
#### 我了解Vim只是一个文本编辑器，但是如果您希望我在不失去焦点的情况下工作并且不时不退出Vim，那么如果我忘记了所有文件名，该怎么办？ (I understand Vim is just a text editor but if you want me to work without losing focus and without exiting Vim every now and then, what options do I have if I can’t remember all the file names?)
Simple, use the file explorer provided by VIM ? Yes, Vim provides a simple file explorer (*without any plugins*). Just type : :Explore from any Vim window and you will see an easy to navigate file explorer which can be navigated using ⬆️ and ⬇️ arrow keys. Press Enter/Return key to open a file/directory. Use :q to exit the explorer and vim. If you do not wish to quit vim and continue working with an open file, you have 3 options:
1. Open the explorer in a horizontal ( :Sexplore ) or vertical ( :Vexplore ) split and exit the explorer using :q
以水平( :Sexplore )或垂直( :Vexplore )分割打开资源管理器，并使用:q退出资源管理器
2. Open the explorer in another tabpage using :Texplore and exit using :q
使用:Texplore在另一个标签页中打开资源管理器，然后使用:q退出
3. Open file explorer in your current window and then unload the current buffer and delete it from the buffer list using :bdel (buffer delete).
在当前窗口中打开文件资源管理器，然后卸载当前缓冲区，并使用:bdel (缓冲区删除)将其从缓冲区列表中删除。
NOTE: You can also use the short command :Ex to open the file explorer
#### 有时我必须在某些行上重复相同的步骤才能编辑某些内容。 我很确定Vim将具有使我能够执行此操作的功能。 我对吗？ (Sometimes I have to repeat same steps on some lines to edit something. I am pretty sure Vim will have some feature that enables me to do this. Am I right?)
100% Right! You are talking about macros and Vim supports macros. Repeating the last executed command is simple and can accomplish simple repetitive tasks. However, if the text processing is made up of several steps to achieve a result, macros come in handy.
100％对！ 您在谈论宏，Vim支持宏。 重复最后执行的命令很简单，并且可以完成简单的重复任务。 但是，如果文本处理由几个步骤组成，以获得一个结果，则宏会派上用场。
Consider an example C header file :
void encrypt_text(char *text, int bytes)
void decrypt_text(char *text, int bytes)
void process_text(char *text, int bytes)
void another_important_function(int bytes, double precision)
Oops! You forgot to put a semicolon at the end of each line and also you just realized that all these functions return an integer error code instead of void.
The steps you need to perform for making change in one line are:
• Place the cursor at the beginning of the word void
将光标放在单词void的开头
• Press cw in normal mode to delete the word void and type int
在正常模式下按cw删除单词void并输入int
• Press Esc , move to the end of line using Shift+a to insert ;
Esc ，使用Shift+a插入到行尾;
• Press Esc and press ^ to return to the beginning of the edited line
Esc ，然后按^键返回到已编辑行的开头
Resulting in:
int encrypt_text(char *text, int bytes);
void decrypt_text(char *text, int bytes)
void process_text(char *text, int bytes)
void another_important_function(int bytes, double precision)
You can just record this sequence of steps and replay it on all 4 lines.
All you have to do is, before you start the sequence, start recording the macro in any alphabet (let’s say a) by pressing qa in normal mode. Now your steps are being recorded in a . Once you are done with all your steps, just press q in normal mode. This will end the recording. To replay these steps, just keep the cursor at the same place where it was placed during macro. Press @a and we’re done! BOOM! Vim will repeat the same steps for you on that line! To repeat it on multiple lines, you can also use @@ after using @a command once
#### 我知道Vim离IDE不远，我可能抱有一些不合理的希望，只是一个简单的问题：Vim是否可以远程编辑文件？ (I know Vim is nowhere close to an IDE and I may be having some unreasonable hopes but just a quick question: Remote editing of files possible with Vim?)
If you think of it considering the available resources:[1] Vim[2] openssh-client (Comes installed with most Linux flavors)
You are in luck my friend! Yes, Vim supports remote editing of files ?Vim just utilizes the secure connection established by scp (secure copy) provided by openssh-client. There are times when you are working with files on multiple remote machines and it’s a waste of time to log into a machine just to edit one single file! You can relax in your current machine if you just know your remote machine credentials and path.
vim scp://remoteuser@remote_IP_or_hostname/relative/path/of/file
For example: I need to edit a file on 10.0.18.12 stored in /home/dev-john/project/src/main.c and I have login credentials for dev-john, I can access the main.c using:
$vim scp://dev-john@10.0.18.12/project/src/main.c I can use the relative path because, I can start looking for the file from the home directory of dev-john 我可以使用相对路径，因为我可以从dev-john的主目录开始查找文件 TIP: If you access a remote machine frequently, you can create an ssh config file to create a shortcut for the connection. Create a file ~/.ssh/config with 提示：如果您经常访问远程计算机，则可以创建一个ssh配置文件来创建连接的快捷方式。 使用以下命令创建文件~/.ssh/config Host remote-dev-machine Hostname 10.0.18.12 User dev-john IdentityFile ~/.ssh/id_rsa Now you can access your file using: 现在，您可以使用以下方式访问文件： $ vim scp://remote-dev-machine/project/src/main.c
If it’s confusing to remember the relative path and not intuitive, you can also specify it with an alternative:
\$ vim scp://remote-dev-machine/~dev-john/project/src/main.c
#### 太棒了！ 我已经为Vim的开箱即用功能感到兴奋。 看起来您已经解决了许多常见的编辑问题。 让我们来看看。 我有一个超过2000行的文件，并且我感兴趣的功能位于第9行，第768行和第1898行。我知道我可以使用行号跳到一行，但是我不太会记住这些数字。 有什么给我的吗？ (Awesome! I’m already thrilled at the out-of-the-box capabilities of Vim. Looks like you’ve a solution to a lot of common editing problems. Let’s see. I have a file with over 2000 lines and the functions of my interest are located at line 9, line 768 and line 1898. I know I can jump to a line using line number but I’m not so good at remembering those numbers. Got anything for me?)
Hell yeah! What you’re looking for is a local bookmark solution in Vim using letters. All you have to do is :
• Place your cursor on any line at any position
将光标放在任何位置的任何行上
• Press Esc to make sure you’re in normal mode
Esc以确保您处于正常模式
• Press m{lowercaseletter} where {lowercaseletter} is any letter from a-z
m{lowercaseletter} ，其中{lowercaseletter}是来自az任何字母
• You just created a local bookmark to navigate in your file
您刚刚创建了本地书签以浏览文件
To view all your bookmarks: Press Esc and enter command mode, type :marks and hit Enter/Return . You’ll see a list of your bookmarks. To visit any bookmark at any time, just press Esc and type {lowercaseletter} . Kaboom! You’ll arrive at the exact same location with cursor where you bookmarked. Example:
I have created a local bookmark to line 21, column 18 using a . If I’m editing something on line 1783, I would just press Esc and type a :
To solve your problem, all you’ve to do is create 3 local bookmarks and quickly jump to them by looking at :marks .
Problem solved ?
What if I told you that you can create global bookmarks too?! ? Yes, it is possible to create global bookmarks too! These are equivalent to your windows or GUI shortcuts (or linux soft/hardlinks) except you don’t need to create an actual link. You heard me right! You can literally jump from editing a file in /dir1 to another file and line in /project/src/ from your Vim without exiting ! ?
Fret not, it’s not a big new thing to remember. All you have to do is:Use an uppercase letter instead of lower case letter to create a global bookmark. That’s all! Really! You navigate to the global bookmark using the same process. Example: If you’ve created a bookmark using mP , all you’ve to do is press Esc and type P and BAM! You jump to your global bookmark (Vim remembers the path, so you don’t have to type anything about the path)
You can access the global bookmarks in the same way as local : :marks
:marks
mark line col file/text
P 53 4 ~/project/src/large-file.c
A 11 0 ~/project/README.md
NOTE: If you are not interested in the cursor position and just want to be there at the beginning of you bookmarked line, use 'P instead of P (Use a single quote instead of back tick to be positioned at the beginning of the line)
#### 我听说Vim支持窗口拆分和选项卡！ 我知道选项卡很棒，您可以一次使用多个打开的文件。 但是，分裂呢？ 我为什么要那个？ (I’ve heard that Vim supports window splitting along with tabs! I understand tabs are great and you get to work with multiple open files at once. But, what about splitting? Why would I want that?)
Scenarios:
• You may want to edit a file by looking at another file simultaneously (May be you are defining a C function by looking at it’s declaration in a header file)
您可能希望通过同时查看另一个文件来编辑文件(可能是通过查看头文件中的声明来定义C函数)
• You may want to edit some portion of a file by looking at the top/bottom portion of the same file simultaneously
您可能希望通过同时查看同一文件的顶部/底部来编辑文件的某些部分
• Your work may require you to edit a file by looking at different portions of different files simultaneously
您的工作可能需要您通过同时查看不同文件的不同部分来编辑文件
Vim supports splitting of screen both horizontally and vertically. Even better, you can even browse file system to open a file when you split your screen.
Vim支持水平和垂直屏幕分割。 更好的是，您甚至可以在拆分屏幕时浏览文件系统以打开文件。
Here are the available options:
:split filename - split window horizontally and load filename
:vsplit file - vertical split and open file
ctrl-w up arrow - move cursor up a window
ctrl-w ctrl-w - move cursor to another window (cycle)
ctrl-w _ - maximize current window vertically
ctrl-w | - maximize current window horizontally
ctrl-w = - make all equal size
:sview file - same as split, but readonly
:close - close current window
Maximizing a window for work:
Resizing:
CTRL-W [N] - Decrease current window height by N (default 1)
CTRL-W [N] + Increase current window height by N (default 1)
CTRL-W [N] < Decrease current window width by N (default 1)
CTRL-W [N} > Increase current window width by N (default 1)
Is there a way to use file explorer while I split panes? (I can’t remember and type the file names always!)
Of course, all you have to do is type : :Sexplore for horizontal file explorer and :Vexplore for vertical file explorer. You can also use :Vexplore! to open the file explorer on right side (instead of default left)
Again, all this works *without any extra plugins* ?
#### 我正在编辑一些代码，因此我很快需要运行一个shell命令。 我应该保存工作，退出Vim并运行命令吗？ 我敢打赌Vim有更好的出路 (I am in the middle of editing some code and I quickly need to run a shell command. Should I save my work, exit Vim and run my commands? I bet there is a better way out with Vim)
You bet! Vim just doesn’t want you to leave Vim and wants you to continue focussing on your work. Hence the option to execute shell commands from within your Vim. Don’t worry, all your unsaved work is not discarded, you just execute your command and BAM! you are back in your unsaved/saved file safely!
Let’s say you are in the middle of a coding session and you quickly need to head out to take a look at man page of file operations because you forgot the signature! You don’t have to save your work, exit Vim and then check man pages or you don’t have to open another tab just for the man page. You can issue the command from right within the Vim editor.
Guess what! Prepare to be amazed. Vim also supports make command from within your file! All you have to do is navigate to a directory with Makefile . Open any file (Could be your source code) and make all the changes and save it. Wait, there’s no need to exit to see the compilation result. You can trigger your make build from right within Vim:
Similarly you can build other targets in your Makefile!
Example: Build directory clean up
I hope these cool features will help you to use Vim more productively.
Feel free to comment, criticize or applaud ?
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2021-10-25 21:21:40
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https://www.reallycutecats.com/2020/11/i-know-im-just-a-cat-but-if-you-feel-sad-ill-be-your-smile-if-you-cry-ill-be-your-comfort-and-if-someone-breaks-your-heart-you-can-use-mine-to-live-ill-always-be-your-side%F0%9F%92%95/
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# I know I’m just a cat, But If you feel sad I’ll be your smile, If you cry, I’ll be your comfort and If someone breaks your heart, you can use mine to live, I’ll always be your side!💕😺 . . . . . . . .
I know I’m just a cat, But If you feel sad I’ll be your smile, If you cry, I’ll be your comfort and If someone breaks your heart, you can use mine to live, I’ll always be your side!💕😺
.
.
.
.
.
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.
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#boristhecat #hungrycat #catlove #cateyes #feline #coolcats #myloveforcats #catishappiness #catsofinstagram #meownation #meow #russiancat #hoomanlove #catsinheart #catsgram
comments
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2021-03-05 22:18:59
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https://everything.explained.today/Euler%e2%80%93Maclaurin_formula/
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# Euler–Maclaurin formula explained
In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus. For example, many asymptotic expansions are derived from the formula, and Faulhaber's formula for the sum of powers is an immediate consequence.
The formula was discovered independently by Leonhard Euler and Colin Maclaurin around 1735. Euler needed it to compute slowly converging infinite series while Maclaurin used it to calculate integrals. It was later generalized to Darboux's formula.
## The formula
If and are natural numbers and is a real or complex valued continuous function for real numbers in the interval, then the integral$I = \int_m^n f(x)\,dx$can be approximated by the sum (or vice versa)$S = f(m + 1) + \cdots + f(n - 1) + f(n)$(see rectangle method). The Euler–Maclaurin formula provides expressions for the difference between the sum and the integral in terms of the higher derivatives evaluated at the endpoints of the interval, that is to say and .
Explicitly, for a positive integer and a function that is times continuously differentiable on the interval, we have$S - I = \sum_^p + R_p,$where is the th Bernoulli number (with) and is an error term which depends on,,, and and is usually small for suitable values of .
The formula is often written with the subscript taking only even values, since the odd Bernoulli numbers are zero except for . In this case we have[1] $\sum_^n f(i) = \int^n_m f(x)\,dx + \frac + \sum_^ \frac \left(f^(n) - f^(m)\right) + R_p,$or alternatively$\sum_^n f(i) = \int^n_m f(x)\,dx + \frac + \sum_^ \frac \left(f^(n) - f^(m)\right) + R_p.$
### The remainder term
See also: Bernoulli polynomials.
The remainder term arises because the integral is usually not exactly equal to the sum. The formula may be derived by applying repeated integration by parts to successive intervals for . The boundary terms in these integrations lead to the main terms of the formula, and the leftover integrals form the remainder term.
The remainder term has an exact expression in terms of the periodized Bernoulli functions . The Bernoulli polynomials may be defined recursively by and, for,$\begin B_k'(x) &= kB_(x), \\ \int_0^1 B_k(x)\,dx &= 0.\end$The periodized Bernoulli functions are defined as$P_k(x) = B_k\bigl(x - \lfloor x\rfloor\bigr),$where denotes the largest integer less than or equal to, so that always lies in the interval .
With this notation, the remainder term equals$R_p = (-1)^\int_m^n f^(x) \frac\,dx.$
When, it can be shown that$\bigl|B_k(x)\bigr| \le \frac\zeta(k),$where denotes the Riemann zeta function; one approach to prove this inequality is to obtain the Fourier series for the polynomials . The bound is achieved for even when is zero. The term may be omitted for odd but the proof in this case is more complex (see Lehmer).[2] Using this inequality, the size of the remainder term can be estimated as$\left|R_p\right| \leq \frac\int_m^n \left|f^(x)\right|\,dx.$
### Low-order cases
The Bernoulli numbers from to are . Therefore the low-order cases of the Euler–Maclaurin formula are:$\begin\sum_^n f(i) - \int_m^n f(x)\,dx &= \frac + \int_m^n f'(x)P_1(x)\,dx \\&=\frac + \frac\frac - \int_m^n f$(x)\frac\,dx \\&=\frac + \frac\frac + \int_m^n f(x)\frac\,dx \\&=\frac + \frac\frac - \frac\frac-\int_m^n f^(x) \frac\, dx \\&=\frac + \frac\frac - \frac\frac + \int_m^n f^(x)\frac\,dx \\&=\frac + \frac\frac - \frac\frac + \frac\frac - \int_m^n f^(x)\frac\,dx \\&=\frac + \frac\frac - \frac\frac + \frac\frac + \int_m^n f^(x)\frac\,dx.\end
## Applications
### The Basel problem
The Basel problem is to determine the sum$1 + \frac14 + \frac19 + \frac1 + \frac1 + \cdots = \sum_^\infty \frac.$
Euler computed this sum to 20 decimal places with only a few terms of the Euler–Maclaurin formula in 1735. This probably convinced him that the sum equals, which he proved in the same year.[3]
### Sums involving a polynomial
See also: Faulhaber's formula. If is a polynomial and is big enough, then the remainder term vanishes. For instance, if, we can choose to obtain, after simplification,$\sum_^n i^3 = \left(\frac\right)^2.$
### Approximation of integrals
The formula provides a means of approximating a finite integral. Let be the endpoints of the interval of integration. Fix, the number of points to use in the approximation, and denote the corresponding step size by . Set, so that and . Then:[4] $\beginI & = \int_a^b f(x)\,dx \\&\sim h\left(\frac + f(x_2) + \cdots + f(x_) + \frac\right) + \frac\bigl[f'(x_1) - f'(x_N)\bigr] - \frac\bigl[f'''(x_1) - f'''(x_N)\bigr] + \cdots\end$
This may be viewed as an extension of the trapezoid rule by the inclusion of correction terms. Note that this asymptotic expansion is usually not convergent; there is some, depending upon and, such that the terms past order increase rapidly. Thus, the remainder term generally demands close attention.[4]
The Euler–Maclaurin formula is also used for detailed error analysis in numerical quadrature. It explains the superior performance of the trapezoidal rule on smooth periodic functions and is used in certain extrapolation methods. Clenshaw–Curtis quadrature is essentially a change of variables to cast an arbitrary integral in terms of integrals of periodic functions where the Euler–Maclaurin approach is very accurate (in that particular case the Euler–Maclaurin formula takes the form of a discrete cosine transform). This technique is known as a periodizing transformation.
### Asymptotic expansion of sums
In the context of computing asymptotic expansions of sums and series, usually the most useful form of the Euler–Maclaurin formula is$\sum_^b f(n) \sim \int_a^b f(x)\,dx + \frac + \sum_^\infty \,\frac \left(f^(b) - f^(a)\right),$
where and are integers.[5] Often the expansion remains valid even after taking the limits or or both. In many cases the integral on the right-hand side can be evaluated in closed form in terms of elementary functions even though the sum on the left-hand side cannot. Then all the terms in the asymptotic series can be expressed in terms of elementary functions. For example,$\sum_^\infty \frac \sim \underbrace_ + \frac + \sum_^\infty \frac.$
Here the left-hand side is equal to, namely the first-order polygamma function defined by
\psi(1)(z)=
d2 dz2
log\Gamma(z);
the gamma function is equal to when is a positive integer. This results in an asymptotic expansion for . That expansion, in turn, serves as the starting point for one of the derivations of precise error estimates for Stirling's approximation of the factorial function.
#### Examples
If is an integer greater than 1 we have:$\sum_^n \frac \approx \frac 1+\frac 12-\frac 1+\frac 1+\sum_\frac\left[\frac{(s+2i-2)!}{(s-1)!}-\frac{(s+2i-2)!}{(s-1)!n^{s+2i-1}}\right].$
Collecting the constants into a value of the Riemann zeta function, we can write an asymptotic expansion:$\sum_^n \frac \sim\zeta(s)-\frac 1+\frac 1-\sum_\frac\frac.$
For equal to 2 this simplifies to$\sum_^n \frac \sim\zeta(2)-\frac 1n+\frac 1-\sum_\frac,$or$\sum_^n \frac \sim \frac -\frac +\frac -\frac+\frac-\frac + \cdots.$
When, the corresponding technique gives an asymptotic expansion for the harmonic numbers:$\sum_^n \frac \sim \gamma + \log n + \frac - \sum_^\infty \frac,$where is the Euler–Mascheroni constant.
## Proofs
### Derivation by mathematical induction
We outline the argument given in Apostol.[6]
The Bernoulli polynomials and the periodic Bernoulli functions for were introduced above.
The first several Bernoulli polynomials are$\begin B_0(x) &= 1, \\ B_1(x) &= x - \tfrac, \\ B_2(x) &= x^2 - x + \tfrac, \\ B_3(x) &= x^3 - \tfracx^2 + \tfracx, \\ B_4(x) &= x^4 - 2x^3 + x^2 - \tfrac, \\ &\,\,\,\vdots\end$
The values are the Bernoulli numbers . Notice that for we have$B_n = B_n(0) = B_n(1),$and for,$B_1 = B_1(0) = -B_1(1).$
The functions agree with the Bernoulli polynomials on the interval and are periodic with period 1. Furthermore, except when, they are also continuous. Thus,$P_n(0) = P_n(1) = B_n \quad \textn \neq 1.$
Let be an integer, and consider the integral$\int_k^ f(x)\,dx = \int_k^ u\,dv,$where$\begin u &= f(x), \\ du &= f'(x)\,dx, \\ dv &= P_0(x)\,dx & \textP_0(x) &= 1, \\ v &= P_1(x).\end$
Integrating by parts, we get$\begin \int_k^ f(x)\,dx &= \bigl[uv\bigr]_k^ - \int_k^ v\,du \\ &= \bigl[f(x)P_1(x)\bigr]_k^ - \int_k^ f'(x)P_1(x)\,dx \\ &= B_1(1)f(k+1)-B_1(0)f(k) - \int_k^ f'(x)P_1(x)\,dx.\end$
Using,, and summing the above from to, we get$\begin\int_0^n f(x)\, dx &= \int_0^1 f(x)\,dx + \cdots + \int_^n f(x)\,dx \\&= \frac+ f(1) + \dotsb + f(n-1) + \frac - \int_0^n f'(x) P_1(x)\,dx.\end$
Adding to both sides and rearranging, we have$\sum_^n f(k) = \int_0^n f(x)\,dx + \frac + \int_0^n f'(x) P_1(x)\,dx.$
This is the case of the summation formula. To continue the induction, we apply integration by parts to the error term:$\int_k^ f'(x)P_1(x)\,dx = \int_k^ u\,dv,$where$\begin u &= f'(x), \\ du &= f$(x)\,dx, \\ dv &= P_1(x)\,dx, \\ v &= \tfracP_2(x).\end
The result of integrating by parts is$\begin \bigl[uv\bigr]_k^ - \int_k^ v\,du &= \left[\frac{f'(x)P_2(x)}{2} \right]_k^ - \frac\int_k^ f$(x)P_2(x)\,dx \\ &= \frac(f'(k + 1) - f'(k)) - \frac\int_k^ f(x)P_2(x)\,dx.\end
Summing from to and substituting this for the lower order error term results in the case of the formula,$\sum_^n f(k) = \int_0^n f(x)\,dx + \frac + \frac\bigl(f'(n) - f'(0)\bigr) - \frac\int_0^n f$(x)P_2(x)\,dx.
This process can be iterated. In this way we get a proof of the Euler–Maclaurin summation formula which can be formalized by mathematical induction, in which the induction step relies on integration by parts and on identities for periodic Bernoulli functions.
## Further reading
• H. W. . Gould . William . Squire . Maclaurin's second formula and its generalization . 1963. Amer. Math. Monthly . 70 . 1 . 44–52. 2312783 . 0146551 . 10.2307/2312783.
• Web site: Gourdon . Xavier. Sebah. Pascal . Introduction on Bernoulli's numbers. 2002.
• Erich . Martensen . On the generalized Euler-Maclaurin formula. Z. Angew. Math. Mech. . 85 . 12 . 858–863 . 10.1002/zamm.200410217 . 2184846 . 2005. 2005ZaMM...85..858M .
• Book: Hugh L. . Montgomery . Hugh Montgomery (mathematician) . Robert C. . Vaughan . Robert Charles Vaughan (mathematician) . Multiplicative number theory I. Classical theory . Cambridge tracts in advanced mathematics . 97 . 2007 . 978-0-521-84903-6 . 495–519.
## Notes and References
1. Web site: Digital Library of Mathematical Functions: Sums and Sequences. National Institute of Standards and Technology.
2. Lehmer. D. H.. D. H. Lehmer . On the maxima and minima of Bernoulli polynomials . 1940 . The American Mathematical Monthly. 47. 8. 533–538 . 10.2307/2303833. 2303833.
3. Book: Pengelley, David J. . 1912.03527 . Dances between continuous and discrete: Euler's summation formula . Washington, DC . 2349549 . 169–189 . Mathematical Association of America . MAA Spectrum . Euler at 300 . 2007.
4. Book: Devries . Paul L. . Hasbrun . Javier E. . A first course in computational physics. . 2nd . Jones and Bartlett Publishers . 2011 . 156.
5. Book: Abramowitz . Milton . Milton Abramowitz . Stegun . Irene A. . Irene Stegun . . . New York . 978-0-486-61272-0 . 1972 . 16, 806, 886.
6. T. M. . An Elementary View of Euler's Summation Formula . . 106 . 1 May 1999 . 5 . 409–418 . 0002-9890. Apostol . 10.2307/2589145. Tom M. Apostol. Mathematical Association of America. 2589145.
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2022-10-02 09:48:38
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https://au.mathworks.com/help/robust/ref/lti.augw.html
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# augw
Plant augmentation for weighted mixed-sensitivity H and H2 loop-shaping design
## Description
example
P = augw(G,W1,W2,W3) computes a state-space model of an augmented LTI plant P(s) with the weighting functions W1(s), W2(s), and W3(s) penalizing the error signal, control signal, and output signal, respectively. P is the augmented plant of the following diagram.
This control structure is used in mixed H synthesis, which lets you design an H controller by simultaneously shaping the frequency responses for tracking and disturbance rejection, noise reduction and robustness, and controller effort. For more information, see Mixed-Sensitivity Loop Shaping.
## Examples
collapse all
Suppose you want to synthesize a stabilizing robust controller for the system of the following diagram. The controller must also reject disturbances injected at the plant output.
The plant, G, is an unstable first-order system.
G = tf(1,[1 -1]);
To set up this problem for hinfsyn, insert a weighting function W1 that captures the disturbance rejection goal, and another weighting function W3 to enforce robustness. Specify these weighting functions as the inverses of the desired loop shapes for the sensitivity S and complementary sensitivity T, respectively. (See Mixed-Sensitivity Loop Shaping.)
For this example, choose W1 with:
• Low-frequency gain of 100 (40 dB)
• 0 dB crossover at 0.5 rad/s
• High-frequency gain of 0.25 (12 dB)
Choose W3 to have the opposite low-frequency and high-frequency gains.
W1 = makeweight(100,[1 0.5],0.25);
W3 = makeweight(0.25,[1 0.5],100);
bodemag(W1,W3)
For this example, do not specify a W2 (no restriction on control effort). Construct the augmented plant, P.
P = augw(G,W1,[],W3);
G has one input and one output. The augmented plant has an additional input for the control signal, and additional outputs for each of the weights.
size(P)
State-space model with 3 outputs, 2 inputs, and 3 states.
The inputs and outputs of P are grouped to keep track of the disturbance and control inputs and the error and measurement outputs. For example, example the output groups. Group Y1 contains the two error outputs z, and group Y2 contains the single measurement output.
P.OutputGroup
ans = struct with fields:
Y1: [1 2]
Y2: 3
You can now use P for control design. For example, use hinfsyn to design an ${\mathit{H}}_{\infty }$ optimal controller that meets the design requirements specified by W1 and W3.
[K,CL,gamma] = hinfsyn(P);
gamma
gamma = 0.9946
## Input Arguments
collapse all
Plant, specified as a dynamic system model such as a state-space (ss) model. G can be any LTI model. If G is a generalized state-space model with uncertain or tunable control design blocks, then mixsyn uses the nominal or current value of those elements.
Weighting functions, specified as dynamic system models. Choose the weighting functions W1,W2,W3 to shape the frequency responses for tracking and disturbance rejection, controller effort, and noise reduction and robustness. Typically:
• For good reference-tracking and disturbance-rejection performance, choose W1 large inside the control bandwidth to obtain small S.
• For robustness and noise attenuation, choose W3 large outside the control bandwidth to obtain small T.
• To limit control effort in a particular frequency band, increase the magnitude of W2 in this frequency band to obtain small KS.
If one of the weights is not needed, set it to []. For instance, if you do not want to restrict control effort, use W2 = [].
Use makeweight to create weighting functions with the desired gain profiles. For details about choosing weighting functions, see Mixed-Sensitivity Loop Shaping.
If G has NU inputs and NY outputs, then W1,W2,W3 must be either SISO or square systems of size NY, NU, and NY, respectively.
Because S + T = I, mixsyn cannot make both S and T small (less than 0 dB) in the same frequency range. Therefore, when you specify weights for loop shaping, there must be a frequency band in which both W1 and W3 are below 0 dB.
## Output Arguments
collapse all
Augmented plant, returned as a state-space (ss) model. P can be any LTI model with inputs [w;u] and outputs [z;y]. augw groups the inputs and outputs of P using the ss properties InputGroup and OutputGroup such that:
• P.InputGroup has field U1 containing the inputs corresponding to w, and field U2 containing the inputs corresponding to u.
• P.OutputGroup has field Y1 containing the outputs corresponding to z, and group Y2 containing the outputs corresponding to e.
Here, {w;u} and {z;e} are the inputs and outputs of P in the following control system.
## Tips
• For H or H2 synthesis, the models G and W1,W2,W3 must be proper. In other words, they must be bounded as $s\to \infty$ (for continuous-time transfer functions) or $z\to \infty$ (for discrete-time transfer functions). Additionally, W1,W2,W3 must be stable. The plant G must be stabilizable and detectable. Otherwise, the resulting P is not stabilizable by any controller.
## Algorithms
augw produces the augmented plant P(s) given by:
$P\left(s\right)=\left[\begin{array}{cc}{W}_{1}& -{W}_{1}G\\ 0& {W}_{2}\\ 0& {W}_{3}G\\ I& -G\end{array}\right]$
The partitioning is embedded using P = mktito(P,NY,NU), which sets the P.InputGroup and P.OutputGroup properties as follows.
[r,c] = size(P);
P.InputGroup = struct('U1',1:c-NU,'U2',c-NU+1:c);
P.OutputGroup = struct('Y1',1:r-NY,'Y2',r-NY+1:r);
### Topics
Introduced before R2006a
Get trial now
|
2021-12-01 18:09:30
|
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|
http://tex.stackexchange.com/questions/72889/alignment-issue
|
Alignment Issue
I am creating my resume in LaTeX and loving it, using new commands and learning many new things. However I am stuck at the top. I am trying to create an output like this ..
I have learnt a bit about indentation and have to learn more about using the geometry package but during my coding (below) I am not able to align like the above image. I have used \noindent and \flushright but each time I use the command the indentation starts with new line making the output different.
%% (c) Shashwat Pant
%% Resume - C.V of Shashwat Pant
%% September 17th 2012
\documentclass[letterpaper,11pt]{article}
%\usepackage{times}
\usepackage{geometry}
\usepackage{hyperref}
\usepackage[empty]{fullpage}
\newcommand{\head}[1]{\noindent \\ \\ \large \bf #1}
\begin{document}
\begin{center}
\bf{\huge Shashwat Pant}\ \end{center}
\hrule
\begin{center} {
} \end{center}
\begin{flushright}
Voice -
\end{flushright}
\end{document}
Apart from the indentation issue, what font package is good for making resume ?
-
You can use minipages:
%% (c) Shashwat Pant
%% Resume - C.V of Shashwat Pant
%% September 17th 2012
\documentclass[letterpaper,11pt]{article}
%\usepackage[charter]{mathdesign}
% \usepackage{charter}
% \usepackage{mathpazo}
\usepackage{kpfonts}
\usepackage{geometry}
\usepackage{hyperref}
\usepackage[empty]{fullpage}
\begin{document}
\begin{center}
\bf{\huge Shashwat Pant}\ \end{center}
\hrule
\begin{minipage}[c]{.15\textwidth}
\end{minipage}%
\hfill
\begin{minipage}[t]{.3\textwidth}
Address line 1 \ Line 2 \ Line 3 \ Line 4 \ Line 5
\end{minipage}%
\hfill
\begin{minipage}[c]{.3\textwidth}
Voice -
\end{minipage}%
\end{document}
For fonts I have added few choices. Which one is better is a very subjective matter. I prefer charter or palatino or kpfonts.
-
Thanks! Was really helpful, will get the minipage under my belt asap. Other than that if i don't use minipage in the Contact Information field and tried using it on the other two, all the text appears to be bold ? Any guess why ? – Shashwat Sep 17 '12 at 13:58
@Shashwat Your \title (\newcommand{\head}[1]{\noindent \\ \large \bf #1} is defined to be bold. If you use it within minipage it is applicable only inside. Removing minipage leaves the command \bf open and every thing after that will become bold. – Harish Kumar Sep 17 '12 at 14:01
But I am not including the other text under my \title command, so why it is considering the other 2 minipage as input ? Is there a way to create a new scope for contact information without using minipage for the first yet keeping the other 2 in minipage while keeping the font normal ? – Shashwat Sep 17 '12 at 14:04
@Shashwat: Effect of \bf will be felt outside the \head command also unless you put inside a group. For example put extra set of braces as in \newcommand{\head}[1]{\par {\large \bf #1}} and see the effect. – Harish Kumar Sep 17 '12 at 14:09
Could you please remove the image/address. I don't want to put in on internet. Thanks – Shashwat Jun 24 '14 at 12:00
Some general comments on the code
\newcommand{\head}[1]{\noindent \\ \\ \large \bf #1}
Try to avoid using \\ at all, and certainly for adding vertical space, this doesn't add vertical space but rather it adds blank lines (which don't stretch and which do the wrong things at page breaks) To add vertical space use \vspace{2\baselineskip} This command does not use any braces so would make any following text be large and bold. Also \bf is a deprecated command only defined in some classes (not in latex itself) for compatibility with the old latex2.09 system.
Better would be
\newcommand{\head}[1]{{\par\large \bfseries \noindent#1\par}}
You should always make sure if using size change commands that the end of the paragraph is in the scope of the size change, otherwise you get large text on a small baseline and irregular spacing.
\begin{center} {
LaTeX environments imply grouping so you don't need (and in some cases must not have) the extra {' group around the environment contents. In this case it is mostly harmless, but it would be better to use simply
\begin{center}
Each of your environments is a full width display, aligned left right or center, so they come one below the other. You want a three column layout, so the simplest thing is to use a table.
\usepackage{array}
....
\begin{tabular}{%
>{\raggedright\large\bfseries}p{3cm}%
>{\centering}p{5cm}%
>{\raggedright\arraybackslash}p{2cm}%
%
Contact Information&
Voice\\
...
\end{tabular}
-
Thanks a lot sir, will keep your tips in mind. As far as {} is concerned, its a bad habit from my C++ coding – Shashwat Sep 17 '12 at 13:59
Another option would be to use tabular-like environments; in the following example I used tabular environments inside a tabularx:
\documentclass[letterpaper,11pt,draft]{article}
\usepackage{tabularx}
\usepackage{booktabs}
\begin{document}
\noindent
\begin{tabularx}{\linewidth}{@{}>{\bfseries}XlX@{}}
\multicolumn{3}{@{}l}{\huge\bfseries Shashwat Pant}
\\ \toprule
Contact Information
&
{
\begin{tabular}[t]{@{}l@{}}
\end{tabular}
}
&
{
\begin{tabular}[t]{@{}l@{}l@{}}
Voice: & \texttt{+}000 99 999 99 \\
Email: & \texttt{email@gmail.com} \\
GitHub: & \texttt{shashpant}
\end{tabular}
}
\\
\end{tabularx}
\end{document}
Unrelated, but useful: never use two consecutive line changing commands \\ \\ (this will produce underfull boxes warnings); instead of the old \bf form, one should use \bfseries in modern LaTeX documents.
-
Thanks, I was looking at tabular representation but can't get hold of some syntax, I prefer to learn the command before implementing so can you please point to some good tabularx document. Other than that when I compile your code I get an awkward placement of the text> I'd really love to use this code, however the awkward alignment and lack of my geometry` class knowledge makes it worse. Image/Screenshot i.imgur.com/zDCgX.png – Shashwat Sep 17 '12 at 13:54
@Shashwat of course; the tabularx package documentation contains the description of the relevant features. Regarding the problem with your actual code, I would need to see the actual code you are using to see where the problem might be. – Gonzalo Medina Sep 17 '12 at 13:57
I copy pasted your code and compiled it, all the text appears to be centered right, while I want text to be appear left centered – Shashwat Sep 17 '12 at 14:06
@Shashwat something else must be going on in your actual code since my example as is doesn't behave like that; again, we need to see the actual code you are using. – Gonzalo Medina Sep 17 '12 at 22:53
Could you please remove the image/address. I don't want to put in on internet. Thanks – Shashwat Jun 24 '14 at 11:59
|
2015-07-07 15:53:17
|
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|
https://socratic.org/questions/what-are-the-absolute-extrema-of-f-x-x-5-x-3-x-2-7x-in-0-7
|
# What are the absolute extrema of f(x)= x^5 -x^3+x^2-7x in [0,7]?
Jul 2, 2017
Minimum: $f \left(x\right) = - 6.237$ at $x = 1.147$
Maximum: $f \left(x\right) = 16464$ at $x = 7$
#### Explanation:
We're asked to find the global minimum and maximum values for a function in a given range.
To do so, we need to find the critical points of the solution, which can be done by taking the first derivative and solving for $x$:
$f ' \left(x\right) = 5 {x}^{4} - 3 {x}^{2} + 2 x - 7$
$x \approx 1.147$
which happens to be the only critical point.
To find the global extrema, we need to find the value of $f \left(x\right)$ at $x = 0$, $x = 1.147$, and $x = 7$, according to the given range:
• $x = 0$: $f \left(x\right) = 0$
• $x = 1.147$: $f \left(x\right) = - 6.237$
• $x = 7$: $f \left(x\right) = 16464$
Thus the absolute extrema of this function on the interval $x \in \left[0 , 7\right]$ is
Minimum: $f \left(x\right) = - 6.237$ at $x = 1.147$
Maximum: $f \left(x\right) = 16464$ at $x = 7$
|
2019-03-24 23:25:31
|
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|
https://www.numerade.com/questions/in-the-circuit-in-fig-p2947-an-emf-of-900-v-is-added-in-series-with-the-capacitor-and-the-resistor-a/
|
🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning Numerade Educator ### Problem 48 Hard Difficulty # In the circuit in Fig. P29.47, an emf of 90.0 V is added in series with the capacitor and the resistor, and the capacitor is initially uncharged. The emf is placed between the capacitor and switch$S$, with the positive terminal of the emf adjacent to the capacitor. Otherwise, the two circuits are the same as in Problem 29.47. The switch is closed at$t =$0. When the current in the large circuit is 5.00 A, what are the magnitude and direction of the induced current in the small circuit? ### Answer ##$1.83 \mathrm{mA}\$
#### Topics
Electromagnetic Induction
Inductance
### Discussion
You must be signed in to discuss.
##### Andy C.
University of Michigan - Ann Arbor
LB
##### Marshall S.
University of Washington
##### Aspen F.
University of Sheffield
Lectures
Join Bootcamp
### Video Transcript
and this question were asked to find the magnitude and direction of the induced current in the small circuit. So the current flow in a charging RC circuit is expressed as the following. I here is equal to V not the initial potential divided by are not multiplied by one minus epsilon. Excuse me. Not absolute e to the minus. I current over our C Uh huh. So therefore, taking the derivative of this d I with respect to t we find that this is equal to minus our potential, which is the induced Ian meth divided by are not squared times the capacitance see times the exponential e to the minus t. So excuse me, this isn't I. This is t divided by R c. Okay, well, the induced e m f is equal to in times the change in the magnetic flux defy d t well, defy d t. So this is still in defy d t is equal to you, not divided by two pi multiplied by the natural log Ellen of one plus oversee multiplied by d i d. T, which we just found to be equal to e divided by are not squared, see times I Okay, so therefore Oh, and I forgot to be here. Therefore I induced which is equal to he induced divided by I am So we need to find this are this are comes from the material It's going to be equal to 25 times 0.6 meters times resistive 81.0 homes for meter So this comes out to equal 15 owes. So now we can plug this value into our equation. So we find I induced is equal to and times the magnetic permeability of free space mu not a times B divided by to pie multiplied by the natural log of one plus the ratio a oversee multiplied by one over the initial resistance are not well supplied by the capacitance See times. The current I multiplied by one over Are we just found OK, so carrying this out, we find that this is equal to 1.83 times 10 to the minus three amps or 1.83 million amps, and it asks us also to find the direction So using the rent law the direction of induced current in the small loop is clockwise direction. That's the direction of induced current in the smaller. But here's clockwise is what we want, right? So we'll just go ahead and type out clockwise plot wise in boxes in as our solution to the question.
University of Kansas
#### Topics
Electromagnetic Induction
Inductance
##### Andy C.
University of Michigan - Ann Arbor
LB
##### Marshall S.
University of Washington
##### Aspen F.
University of Sheffield
Lectures
Join Bootcamp
|
2021-07-25 23:14:37
|
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|
https://iccl.inf.tu-dresden.de/web/Article4010
|
# (Non-)Succinctness of uniform interpolants of general terminologies in the description logic ℰℒ
##### Nadeschda NikitinaNadeschda Nikitina, Sebastian RudolphSebastian Rudolph
Nadeschda Nikitina, Sebastian Rudolph
(Non-)Succinctness of uniform interpolants of general terminologies in the description logic ℰℒ
Artificial Intelligence, 215:120-140, October 2014
• KurzfassungAbstract
ℰℒ is a popular description logic, used as a core formalism in large existing knowledge bases. Uniform interpolants of knowledge bases are of high interest, e.g. in scenarios where a knowledge base is supposed to be partially reused. However, to the best of our knowledge no procedure has yet been proposed that computes uniform ℰℒ interpolants of general ℰℒ terminologies. Up to now, also the bound on the size of uniform ℰℒ interpolants has remained unknown. In this article, we propose an approach to computing a finite uniform interpolant for a general ℰℒ terminology if it exists. To this end, we develop a quadratic representation of ℰℒ TBoxes as regular tree grammars. Further, we show that, if a finite uniform ℰℒ interpolant exists, then there exists one that is at most triple exponential in the size of the original TBox, and that, in the worst case, no smaller interpolants exist, thereby establishing tight worst-case bounds on their size. Beyond showing these bounds, the notions and results established in this paper also provide useful insights for designing efficient ontology reformulation algorithms, for instance, within the context of module extraction.
• Weitere Informationen unter:Other info: Link
• Forschungsgruppe:Research Group: Computational Logic
@article{NR2014,
author = {Nadeschda Nikitina and Sebastian Rudolph},
title = {(Non-)Succinctness of uniform interpolants of general terminologies
in the description logic {$\mathcal{EL}$}},
journal = {Artificial Intelligence},
volume = {215},
year = {2014},
month = {October},
pages = {120-140},
doi = {10.1016/j.artint.2014.06.005}
}
|
2018-06-21 21:44:58
|
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|
https://blog.acolyer.org/2019/06/28/machine-learning-systems-are-stuck-in-a-rut/
|
# Machine learning systems are stuck in a rut
Machine learning systems are stuck in a rut Barham & Isard, HotOS’19
In this paper we argue that systems for numerical computing are stuck in a local basin of performance and programmability. Systems researchers are doing an excellent job improving the performance of 5-year old benchmarks, but gradually making it harder to explore innovative machine learning research ideas.
The thrust of the argument is that there’s a chain of inter-linked assumptions / dependencies from the hardware all the way to the programming model, and any time you step outside of the mainstream it’s sufficiently hard to get acceptable performance that researchers are discouraged from doing so.
Take a simple example: it would be really nice if we could have named dimensions instead of always having to work with indices.
Named dimensions improve readability by making it easier to determine how dimensions in the code correspond to the semantic dimensions described in, .e.g., a research paper. We believe their impact could be even greater in improving code modularity, as named dimensions would enable a language to move away from fixing an order on the dimensions of a given tensor, which in turn would make function lifting more convenient…
For the readability point I feel I ought to mention you could always declare a ‘constant’ , e.g FEATURE_NAME = 1, and use that to make your code more readable (constant is in quotes there because Python doesn’t really have constants, but it still has variable names!). But that won’t solve the ordering issue of course.
It would be interesting to explore unordered sets of named dimensions in the programming model and see what benefits that could bring, however,…
It is hard to experiment with front-end features like named dimensions, because it is painful to match them to back ends that expect calls to monolithic kernels with fixed layout. On the other hand, there is little incentive to build high quality back ends that support other features, because all the front ends currently work in terms of monolithic operators.
Named dimensions are an easy to understand example, but the challenges go much deeper than that, and were keenly felt by the authors during research on Capsule networks.
### Challenges compiling non-standard kernels
Convolutional Capsule primitives can be implemented reasonably efficiently on CPU but problems arise on accelerators (e.g. GPU and TPU). Performance on accelerators matters because almost all current machine learning research, and most training of production models, uses them.
Scheduling instructions for good performance in accelerators is a complex business. It’s “very challenging” just for standard convolutions, and convolutional capsules add several dimensions of complexity. Because it’s so tricky, high-performance back-ends for accelerators tend to spend a lot of effort optimising a small set of computational kernels.
New primitives that don’t fit into these existing kernels can be compiled into custom kernels using e.g. Tensor Comprehensions or PlaidML, but the current state-of-the-art only really supports small code fragments and frequently doesn’t get close to peak performance (e.g. a factor of 8x slower after a one hour search, for a conventional 2D convolution the authors used as an experiment).
Our interpretation of these results is that current frameworks excel at workloads where it makes sense to manually tune the small set of computations used by a particular model or family of models. Unfortunately, frameworks become poorly suited to research, because there is a performance cliff when experimenting with computations that haven’t previously been identified as important.
That said, after around 17 minutes Tensor Comprehensions does find a solution that outperforms a hand-tuned CUDA solution. Which doesn’t seem so bad, until you remember this is just one kernel out of what may be a large overall computation.
The easiest and best performing solution for convolutional Capsules in both TensorFlow and PyTorch turns out to be to target high-level operations already supported by those frameworks. This comes at a cost though; copying, rearranging, and materialising to memory two orders of magnitude more data than is strictly necessary.
### Challenges optimising whole programs
It might be hard to performance tune a single non-standard kernel, but full programs must typically evaluate a large graph of kernels. In order to make use of pre-optimised kernels, it’s necessary to use one of a small number of parameter layouts that have been chosen ahead of time to be optimal in isolation.
In practice there are so few choices of layout available that frameworks like XLA and TVM do not attempt a global layout assignment, and instead choose fixed layouts for expensive operators like convolution, then propagate those layouts locally through the operator graph inserting transposes where necessary.
Similar considerations make it hard to experiment with different choices for quantised and low-precision types.
Whole program optimisations such as common sub-expression elimination are attractive for machine learning, but hard to exploit to the fullest extent with the current state-of-the-art: “it seems likely that it will be necessary to architect machine learning frameworks with automatic optimizers in mind before it will be possible to make the best use of whole-program optimization.
### Challenges evolving programming languages
Recall that back ends are structured around calls to large monolithic kernels. In this section we argue that this back-end design approach is slowing progress in the maintainability, debuggability, and expressiveness of programming models. Worse, the resulting brake on innovation in languages is in itself reducing the incentive for back-end developers to improve on the current situation.
We saw one such example at the top of this piece: support for named dimensions. Another consequence is the choice of kernels or ‘operators’ as the dominant abstraction, with user programs in Python calling into operators written in terms of specific back-end languages and libraries. This tends to fix both the set of operators and also their interfaces.
### Breaking out of the rut
Our main concern is that the inflexibility of languages and back ends is a real brake on innovative research, that risks slowing progress in this very active field…
How might we break out of the rut?
• Embrace language design including automatic differentiation, using purely named dimensions and kernels expressed within the language syntax
• Support a back-end IR defining a graph of layout-agnostic general purpose loop nests
• Use transformation passes over the IR to lower it to a concrete common sub-expression elimination strategy, with layouts for each materialised intermediate
• Compilation passes that generate accelerator code given the lowered IR, with adequate code produced quickly and close to peak performance achievable after searching
At a high level, this reminds me a little of the approach taken by Musketeer.
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2021-01-18 18:53:19
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https://studydaddy.com/question/hcs-465-week-4-dq-2
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QUESTION
# HCS 465 Week 4 DQ 2
This paperwork of HCS 465 Week 4 Discussion Question 2 shows the solutions to the following problems:
What is the meaning of the 2 terms: RELIABILITY and VALIDITY ,as uniquely used in the research process? Be sure to check the text for the definitions.
Provide an example of each & how they would be used in your workplace.
• @
Tutor has posted answer for $5.19. See answer's preview$5.19
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2018-04-25 20:15:34
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https://datascience.stackexchange.com/questions/11763/why-does-an-l2-penalty-prefer-smaller-and-more-diffuse-weight-vectors
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# Why does an L2 penalty prefer smaller and more diffuse weight vectors?
For instance, why is it that it is more favourable for a weight of [0.25, 0.25, 0.25, 0.25] (for which the L2 penalty is 0.25) instead of simply [1, 0, 0, 0] (for which an L2 penalty is 1)?
In this case, both weights would give the same dot product when using W.T * X
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2021-08-05 05:17:01
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http://imkean.com/Hihocoder-1291-Building-in-Sandbox/
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## Hihocoder 1291 Buiding in Sandbox
04/07/2016 题解 OJ 校园招聘 Microsoft 微软在线笔试 Hihocoder BFS
## 描述
Little Hi is playing a sandbox voxel game. In the game the whole world is constructed by massive 1x1x1 cubes. The edges of cubes are parallel to the coordinate axes and the coordinates (x, y, z) of the center of each cube are integers.
At the beginning there is nothing but plane ground in the world. The ground consists of all the cubes of z=0. Little Hi needs to build everything by placing cubes one by one following the rules:
1. The newly placed cube must be adjacent to the ground or a previously placed cube. Two cubes are adjacent if and only if they share a same face.
2. The newly placed cube must be accessible from outside which means by moving in 6 directions(up, down, left, right, forward, backward) there is a path from a very far place - say (1000, 1000, 1000) in this problem - to this cube without passing through ground or other cubes.
Given a sequence of cubes Little Hi wants to know if he can build the world by placing the cubes in such order.
## 输入
The first line contains the number of test cases T(1 <= T <= 10). For each test case the first line is N the number of cubes in the sequence. The following N lines each contain three integers x, y and z indicating the coordinates of a cube. For 20% of the data, 1 <= N <= 1000, 1 <= x, y, z <= 10. For 100% of the data, 1 <= N <= 100000, 1 <= x, y, z <= 100.
## 输出
For each testcase output “Yes” or “No” indicating if Little Hi can place the cubes in such order.
## 样例提示
In the first test case three cubes are placed on the ground. It’s OK. In the second test case (1, 3, 2) is neither on the ground nor adjacent to previous cubes. So it can’t be placed. In the last test case (2, 2, 1) can not be reached from outside. So it can’t be placed.
3
3
1 1 1
1 2 1
1 3 1
3
1 1 1
1 2 1
1 3 2
17
1 1 1
1 2 1
1 3 1
2 3 1
3 3 1
3 2 1
3 1 1
2 1 1
2 1 2
1 1 2
1 2 2
1 3 2
2 3 2
3 3 2
3 2 2
2 2 2
2 2 1
Yes
No
No
BFS
## 代码
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
using std::max;
using std::queue;
const int MAXN = 128;
const int OUTER = 0x3fffffff;
int cube[MAXN][MAXN][MAXN];
int cnt = 0;
int vis[MAXN][MAXN][MAXN] = {0};
int data[100000 + 5][3];
const int dx[] = {0, 0, 1, -1, 0, 0};
const int dy[] = {0, 0, 0, 0, 1, -1};
const int dz[] = {1, -1, 0, 0, 0, 0};
bool bfs(int x, int y, int z, int lim);
struct State {
int x, y, z;
State() : x(0), y(0), z(0)
{ }
State(int a, int b, int c) : x(a), y(b), z(c)
{ }
};
bool adjacent(int x, int y, int z)
{
int a, b, c;
if (z == 1) return true;
for (int i = 0; i < 6; i++)
{
a = x + dx[i];
b = y + dy[i];
c = z + dz[i];
if (a > 0 && b > 0 && c > 0 && cube[a][b][c])
return true;
}
return false;
}
int main()
{
int t, x, y, z, flag, lim;
scanf("%d", &t);
while (t--)
{
lim = 0;
flag = 1;
scanf("%d", &cnt);
memset(cube, 0, sizeof(cube));
memset(vis, 0, sizeof(vis));
for (int i = 0; i < cnt; i++)
{
scanf("%d%d%d", &x, &y, &z);
{
//printf("err: %d %d %d \n",x,y,z);
flag = 0;
}
cube[x][y][z] = (i + 1);
data[i][0] = x;
data[i][1] = y;
data[i][2] = z;
lim = max(max(lim, x), max(y, z));
}
lim += 2;
if (flag)
{
cube[lim][lim][lim] = cnt + 1;
bfs(lim, lim, lim, lim);
while (cnt-- && flag)
flag = bfs(data[cnt][0], data[cnt][1], data[cnt][2], lim);
}
if (flag)
puts("Yes");
else
puts("No");
}
return 0;
}
bool bfs(int x, int y, int z, int lim)
{
queue<State> *que_ptr = new queue<State>();
queue<State> &que = *que_ptr;
que.push(State(x, y, z));
const int value = cube[x][y][z];
cube[x][y][z] = OUTER;
vis[x][y][z] = value;
bool ret = false;
State now;
int a, b, c;
while (!que.empty())
{
now = que.front();
que.pop();
x = now.x;
y = now.y;
z = now.z;
for (int i = 0; i < 6; i++)
{
a = x + dx[i];
b = y + dy[i];
c = z + dz[i];
if (a < 0 || b < 0 || c < 1 || a > lim || b > lim || c > lim)
continue;
if (vis[a][b][c] != value && cube[a][b][c] == OUTER)
ret = true;
if (vis[a][b][c] || cube[a][b][c])
continue;
vis[a][b][c] = value;
cube[a][b][c] = OUTER;
que.push(State(a, b, c));
}
}
delete que_ptr;
return ret;
}
/**
5
3
1 1 1
1 2 1
1 3 2
17
1 1 1
1 2 1
1 3 1
2 3 1
3 3 1
3 2 1
3 1 1
2 1 1
2 1 2
1 1 2
1 2 2
1 3 2
2 3 2
3 3 2
3 2 2
2 2 2
2 2 1
**/
|
2018-08-21 21:16:07
|
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|
https://www.appropedia.org/Compressed_earth_brick_press
|
Project data
This project is an exploration of compressed earth bricks. Mostly because they're awesome.
CCAT, the campus center for appropriate technology, has recently relocated and their new grounds have many uncontrolled hillsides. With general erosion problems and hazards posed by downhill water flow over clay, the need for retaining walls is immediate.
## Literature Review
### Compressed Earth Brick (CEB) basics
Compressed earth bricks are building blocks formed from stabilized or un-stabilized compressed earth. The compression ranges from several hundred pounds total, to several tons. Because of the great gains in durability un-stabilized bricks are only used where nothing is available to stabilize the bricks. In addition to stabilization, the earth the bricks are to be made from is calibrated for durability, workability, and survivability.
When a brick is compressed it loses 30% of its volume. This is due to the mechanical compression of the press driving out air pockets and aligning wet clay particles and compacting the clay around the sand particles.[1]
### Stabilization
There are many stabilizers that can be used. They can be broadly classed into natural and manufactured. They include such wondrous things as plant juices, whey, resins, molasses, wood ashes, and lime just to name a very few. Here in the United States, the presence and low cost of cement makes it both physically and economically efficient.[1][2] Some sources don't even recommend using stabilizers other than cement even when building in developing countries[3]
### Paper as a stabilizer
Papercrete, a cement and paper building material, has been fairly well researched and tested.[2] The paper in papercrete is proported to have great effect as a stabilizer. Amongst the problems with papercrete are, mold, shrinkage, and slow drying time.[3][1]
## Criteria
Teamwork 7 7 51%
Sustainability 7 7 99%
Experimentation 10 10 92%
Product Bricks 2 6 49%
Budget 4 1 82%
repeatability 10 10 84%
Educational 10 10 100%
In the end, process won out over product. Only about three dozen bricks have been made so far. That said, I am quite happy with the experience and the primary goals, education, experimentation, and repeatability, were satisfactorily met.
## Cost
Stuff Cost
Sand (sadly, after late game decision against on-site sand =(purchased) 30$Cement 45$
Boric Acid(as ortho boric acid from coachroach poison) 6$Trashcan(longlife) 30$
Plywood 30$Rakes(2) 30$
Shovels 20$gloves 10$
Storage Structure 130$TOTAL (approximate) 315$
## Preparation
### Earth calibration
After testing your soil, preferably in multiple locations, you will have an earth mix that is about 75% sand and at least 10% clay and less than 35% clay, by volume.[1] The amount of cement needed will be relational to how close you are to this ideal, ranging from 3-5% to 10%..[1] Now to think about making some compressed earth bricks...
### Earth Testing
After reading about all of the tests, about 6 are apparently widely in use, I settled on the two most simple. I chose, the 'block test' and 'salt water test'.
#### The block test
The block test is simply, to make a block out of your earth and measure the shrinkage. This requires a long ish box, think over a foot by 4 inches by four inches. The sides of the box must be slippery so use an oil if the sides are rough. Three block tests, pre-shrinkage
#### The salt water test
To perform this test: add salt and water to a least a cup of your soil in a clear container. Use a teaspoon ish of salt per cup of earth and cover the earth with water. Shake it up. Let it sit for about half an hour. Observe and measure earth separation.
as per:
Fig 1: clear container + Salt Fig 2: add dirt, shake, then let it sit Fig 3: measure the stuff
### Preface to Ram operation
This is ideally a group activity. A minimum of two people are needed to operate a CINVA-ram. Four people is nice, six people is ideal in my experience. I will briefly describe a non-mechanical brick forming method that doesn't require any more than personal conviction, and minimal tools.
### Materials needed (for non-mechanized mixing)
• metal rake
• several buckets(1-3)
• mixing surface(sheet of plywood, where available, to avoid mixing with cement on ground)
• marker
• shovel
• measurer (ruler, tape measure, stick, etc.)
You will need to determine your mix as it relates to your buckets. If you are mixing down your earth with clay or sand you should be able to use the same method I've used to determine approximate cement quantities.
First, fill a bucket full of earth mixture, deposit this bucket on mixing surface. Fill the bucket again, but only to half full, use marker to mark half way point with line all the way around, label line. For that mater, label everything. This is a group activity and as such labels will help to avoid confusion and error. Deposit the second bucket on the mixing surface, form one pile, divide this pile into 10 equal piles. This may take a little work, don't try for perfection, do a decent job of it and proceed. Carefully place one of the piles into the bucket, make tiny tick marks around the bucket at height of the soil. Repeat this process twice more. Approximate these ticks measure. Now draw a line, up this measured distance from your half way line. Label this new line, which should be some small distance above your half way line, 'cement'. This gives you approximately ten percent cement stabilization when measuring. If you are testing to determine best mix ratio, vary your cement input from 10% to 5% by halving the distance between the 'earth' and the cement lines. Then again halved between the 5% test line and the 10% line. Some documentation points to the possibility of getting the cement percentages as low as two percent. However, if you are using another stabilizer you will likely have to use twice as much.
Now to actually go about making some compressed earth bricks...
## Project
I attempted to employ the old "workshop = group labor camp" ploy, with limited success. The most successful work group ended up being my engineering 305 class. In general I have to say that I have grown to believe that most Americans are not particularly good at physical labor anymore. The literature proposes that the CINV-ram we have used, which by the way was made in Bogotá, Colombia, can produce between 40 and 60 blocks per hour.[1] The best performance we could squeeze from it was about a quarter of that, with a 14 person team.
Task Number of People Digging 4 3 2 2 1 1 1 Transporting 3 2 2 Measuring and Testing 1 2 2 2 1 Mixing 2 Filling and leveling 1 1 1 Pressing 1 1 2 1 1 Raising out 1 1 Removing and placing to dry 2 1 Total Human Power 15 10 8 6 3 2
Teamwork means that there should be a smooth flow (See Table above) of:
Digging Harvesting the earth from the best site, doing a rough sort, picking out big rocks and plant mater. Moving Transporting the earth from the harvesting site to the mesuring/sorting/mixing site. Batching Filling the buckets to the appropriate lines. Mixing Evenly distributing the cement, or other stabilizer, with the rest of the earth. Testing Drop testing the mix to ensure proper moisture level, adding water as necessary. Filling Filling the void in the press, keeping the press area tidy. Compressing Operating the press levers to compact brick. Releasing Operating the press levers to release the brick. Removing and Transporting – Pulling the brick from the press operation and moving it to the storage area. Stacking Stacking the bricks and setting aside any broken bricks for reprocessing.
Smooth flow requires adaptation. Jobs overlap, bottlenecks naturally occur, people get tired, communication and fluidity of everyone's role are the tools that craft an efficient teamwork system, which is one of the funnest things ever.
### Press operation is as follows
And remember to water your bricks! Concrete takes Weeks if not months to fully set up. At minimum keep wet for two weeks.
Mix well, but not too well... Team work makes smiles While working, it is best to practice your bigfoot pose as much as possible
## Experimentation
The compressed paper stabilized bricks that I formed are still curing, I will keep them wet(so the cement can cure) and test them in a month. That said, paper made the bricks much more durable out of the press. Processing the paper for mixing was exhaustive. I used a plastic trash can to store the paper in water.
I added an eighth cup of boric acid to the mixture of 50 gallons of paper and water to prevent molding. Molding is widely pointed to as a problem with paper-crete (the product closest to what I'm experimenting with)[4]. Yet, boric acid can be used as a human safe, anti mold agent.[5]. My paper/water/boric acid mix has been easy to handle and mold free for six weeks so far.
adding ortho boric acid let some water drip out this may not be the best way...
I blended the paper in the water after a week with a drill mounted mixing blade. Then again after another week. I then laid it to dry on a screen atop a pallet.
After dry I crumbled it into a bucket and used the drill mixer again to reduce the particle size. I would rate this process as marginally successful. Far too much time invested, and the end product did not have small enough particle size for even distribution.
## Discussion
This is a cursory look at compressed earth brick technology. The technology has become dominated by industry and all of my references are a decade or more old.
While the process is resource conservative, it is labor and time intensive.
My interest in new materials that are 'hyper' efficient is ever persistent, feel free to contact me with questions and comments. eghant atgmail d0tc0m
## References
1. Stulz, Roland, and Kiran Mukerji. Appropriate Bulding Materials. 3rd ed. UK: Swiss Centre for Development Cooperation in TEchnology and Management, 1993.
2. Spense, R.j.s., and D.j. Cook. Building Materials in Developing Countries. New York: John Wiley and Sons, 1983.
3. Crystal.Netbook. Federal Ministry for Economic Cooperation and Development. http://web.archive.org/web/20201123183930/http://www.crystal-netbook.info/
|
2022-08-14 04:08:44
|
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|
https://empymod.emsig.xyz/en/stable/gallery/fdomain/magnetotelluric.html
|
# Magnetotelluric data#
The magnetotelluric (MT) method is a passive method using as a source variations in Earth’s magnetic field, which create telluric currents in the Earth. The variation of Earth’s magnetic field has many origins, e.g., lightning or the interaction between the Earth’s magnetic field and solar wind.
Ubiquitous in MT is the plane-wave approximation, hence, that the source signal is a plane wave hitting the Earth’s surface. Having a 1D source (vertical plane wave) for a layered, 1D model reduces the computation of the impedances and from there the apparent resistivity and apparent phase a simple recursion algorithm. As such it does not make sense to use a full EM wavefield algorithm with three-dimensional sources such as empymod to compute MT responses. However, it is still interesting to see if we can compute MT impedances with a three-dimensional point source.
As background theory we reproduce here Equations (11) to (17) from Pedersen and Hermance (1986), with surrounding text. For a more in-depth read we refer to Chave and Jones (2012).
If we define the impedance as
(1)#$Z = E_x / H_y \, ,$
[…] we can develop a recursive relationship for the impedance at the top of the j-th layer looking down
(2)#$Z_j = z_{oj} \frac{1-R_j \exp(-2\gamma_j t_j)}{1+R_j \exp(-2\gamma_j t_j)} \, , \quad j = N-1, \dots, 1 \, ,$
where
(3)#$z_{oj} \equiv \text{intrinsic impedance} \equiv \sqrt{\rm{i}\omega \mu \rho_j} \, ,$
(4)#$R_j \equiv \text{reflection coefficient} \equiv \frac{z_{oj} - Z_{j+1}}{z_{oj} + Z_{j+1}} \, ,$
$t_j = \text{thickness of layer} j \, ,$
and the impedance at the surface of the deepest layer ($$j=N$$) is given by
(5)#$Z_N = z_{oN}\, .$
The surface impedance, $$Z_j$$, is found by applying Equation (2) recursively from the top of the bottom half-space, $$j = N$$, and propagating upwards. From the surface impedance, $$Z_1$$, we can then calculate the apparent resistivity, $$\rho_a$$, and phase, $$\theta_a$$, as
(6)#$\rho_a = \frac{|Z_1|^2}{\omega \mu} \, ,$
(7)#$\theta_a = \tan^{-1}\frac{\Im(Z1)}{\Re(Z_1)} \, .$
This calculation is repeated for a range of periods and is used to model the magnetotelluric response of the layered structure.
Reference:
import empymod
import numpy as np
import matplotlib.pyplot as plt
from scipy.constants import mu_0
plt.style.use('ggplot')
## Define model parameter and frequencies#
resistivities = np.array([2e14, 300, 2500, 0.8, 3000, 2500])
depths = np.array([0, 200, 600, 640, 1140])
frequencies = np.logspace(-4, 5, 101)
omega = 2 * np.pi * frequencies
### 1D-MT recursion following Pedersen & Hermance#
Using the variable names as in the paper.
# Initiate recursive formula with impedance of the deepest layer.
Z_j = np.sqrt(2j * np.pi * frequencies * mu_0 * resistivities[-1])
# Move up the stack of layers till the top (without air).
for j in range(depths.size-1, 0, -1):
# Thickness
t_j = depths[j] - depths[j-1]
# Intrinsic impedance
z_oj = np.sqrt(1j * omega * mu_0 * resistivities[j])
# Reflection coefficient
R_j = (z_oj - Z_j) / (z_oj + Z_j)
# Exponential factor
gamma_j = np.sqrt(1j * omega * mu_0 / resistivities[j])
exp_j = np.exp(-2 * gamma_j * t_j)
# Impedance at this layer
Z_j = z_oj * (1 - R_j * exp_j) / (1 + R_j * exp_j)
# Step 3. Compute apparent resistivity last impedance
apres_mt1d = abs(Z_j)**2/(omega * mu_0)
phase_mt1d = np.arctan2(Z_j.imag, Z_j.real)
## 1D MT using empymod#
The above derivation and code assume plane waves. We can “simulate” plane waves by putting the source _very_ far away. In this example, we set it one million km away in all directions. As the impedance is the ratio of the Ex and Hy fields the source type (electric or magnetic) and the source orientation do not matter; hence, it can be an arbitrarily rotated electric or magnetic source, the apparent resistivity and apparent phase will always be the same.
dist = 1_000_000_000 # 1 million kilometer (!)
inp = {
'src': (-dist, -dist, -dist),
'rec': (0, 0, 0.1),
'res': resistivities,
'depth': depths,
'freqtime': frequencies,
'verb': 1,
}
# Get Ex, Hy.
ex = empymod.dipole(ab=11, **inp)
hy = empymod.dipole(ab=51, **inp)
# Impedance.
Z = ex/hy
# Apparent resistivity and apparent phase.
apres_empy = abs(Z)**2 / (omega * mu_0)
phase_empy = np.arctan2(Z.imag, Z.real)
## Plot results#
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 4))
ax1.set_title('Apparent resistivity')
ax1.plot(frequencies, apres_mt1d, label='MT-1D')
ax1.plot(frequencies, apres_empy, '--', label='empymod')
ax1.set_xscale('log')
ax1.set_yscale('log')
ax1.set_xlabel('Frequency (Hz)')
ax1.set_ylabel(r'Apparent resistivity ($\Omega\,$m)')
ax1.legend()
ax2.set_title('Phase')
ax2.plot(frequencies, phase_mt1d*180/np.pi)
ax2.plot(frequencies, phase_empy*180/np.pi, '--')
ax2.set_xscale('log')
ax2.yaxis.tick_right()
ax2.set_xlabel('Frequency (Hz)')
ax2.set_ylabel('Phase (degree)')
ax2.yaxis.set_label_position("right")
fig.tight_layout()
fig.show()
empymod.Report()
Sat Oct 15 19:17:59 2022 UTC OS Linux CPU(s) 2 Machine x86_64 Architecture 64bit RAM 7.6 GiB Environment Python File system ext4 Python 3.8.6 (default, Oct 19 2020, 15:10:29) [GCC 7.5.0] numpy 1.23.4 scipy 1.9.2 numba 0.56.3 empymod 2.2.1 IPython 8.5.0 matplotlib 3.6.1
Total running time of the script: ( 0 minutes 1.049 seconds)
Estimated memory usage: 9 MB
Gallery generated by Sphinx-Gallery
|
2023-02-04 02:47:47
|
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|
http://hal.archives-ouvertes.fr/view_by_stamp.php?label=UNIV-MRS1&langue=en&action_todo=view&id=hal-00609697&version=1
|
4462 articles – 13150 references [version française]
HAL: hal-00609697, version 1
arXiv: 1107.3826
Algebra properties for Sobolev spaces- Applications to semilinear PDE's on manifolds
In this work, we aim to prove algebra properties for generalized Sobolev spaces $W^{s,p} \cap L^\infty$ on a Riemannian manifold, where $W^{s,p}$ is of Bessel-type $W^{s,p}:=(1+L)^{-s/m}(L^p)$ with an operator $L$ generating a heat semigroup satisfying off-diagonal decays. We don't require any assumption on the gradient of the semigroup. To do that, we propose two different approaches (one by a new kind of paraproducts and another one using functionals). We also give a chain rule and study the action of nonlinearities on these spaces and give applications to semi-linear PDEs. These results are new on Riemannian manifolds (with a non bounded geometry) and even in the Euclidean space for Sobolev spaces associated to second order uniformly elliptic operators in divergence form.
|
2013-05-24 12:18:17
|
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|
https://gorchilin.com/articles/energy/condenser_2?lang=en
|
Research website of Vyacheslav Gorchilin
2019-07-25
Electrostatic condenser. Calculation schemes
For the correct calculation of electric circuits, we need a model of the electrostatic capacitor (ESC), details of which we discussed in the previous part of this work. Unfortunately, to get a model is not possible because the ESC, and the associated reference system, previously simply was not considered. Let's calculate it yourself.
Model ESK
Model dvuhkletevogo conventional capacitor is shown in figure (3a), and its reactance in the steady circuits is given by: $X_{Cs} = {1 \over \Bbb{i} \omega C_S} \qquad (2.1)$ where: $$\Bbb{i}$$ is the imaginary unit, indicating a phase shift of 90 degrees, $$\omega$$ angular frequency, which is associated with the usual way: $$\omega = 2\pi f$$, and $$C_S$$ is the capacitance of this capacitor.
From previous part we know that the HSC is composed of three tanks, one conventional and two — solitary. For the calculation of electronic circuits it is necessary that all the capacity was doobsledovanie, so our model will consist of a capacitor of $$C_S$$, whose capacity equal to the capacity between two of its plates, and capacitor $$C_1 C_2$$, which in the scheme as well — duroblade, but has a secluded capacitance value of the first and second electrode, respectively (Fig. 3b). Also, there will be a source of charges that the scheme is designated as source voltage $$U_g$$, connected in series with $$C_2$$. In this model, we combine two independent reference systems and assume that for lone tanks the second surface is Land, so the schema specifies the mandatory grounding. It will be assumed in the idealized calculations, though not explicitly shown.
Fig.3. Model conventional and electrostatic capacitor for the calculation of diagrams (a-c). Double-circuit scheme for ESCOs (d).
Remembering the formula (1.2), and the conclusion from the previous section on the phase shift, we can enter a specific value for a new source of tension: $U_g = \Bbb{i} U_1 \frac{C_1}{C_2} \qquad (2.2)$ Recall that $$\Bbb{i}$$ is the imaginary unit, indicating a positive phase shift of 90 degrees. This is different calculation schemes of the alternating current with fixed settings by using complex numbers: in order to show a positive phase shift, a sufficient parameter (current, voltage or resistance) multiplied by $$\Bbb{i}$$, and to show negative on $$\Bbb{i}$$ with a minus sign. Shift 180 degrees to reflect the even easier: it is necessary before setting a minus sign [1,2].
Interestingly, this additional source of charge is never taken into account in the calculation of the diagrams in theoretical electrical engineering, although it is known that electrostatic induction can often be the cause of failure of some elements of the radio equipment. Next, we will try to turn this disadvantage into an advantage and use this effect on purpose.
Energy model validation
Let's check the power ratio of such a source. Imagine independent from the further presentation of the picture and consider a capacitor of $$C_2$$ and the source of $$U$$ separately from the rest of the circuit (Fig. 3c). Let the capacitor is discharged, and the source changed my voltage jump from zero to $$U_g$$. Then the energy of full charge the capacitor will be known formula: $W = \frac{C_2 |U_g|^2}{2}$ the Energy released at the active load $$r$$ is exactly the same. In relation to the algorithm shown in figure (2) from the previous section, we know that $$|U_g| = |U_1| \frac{C_1}{C_2}$$ and charge $$C_2$$ is the same as for $$C_1$$: $$q_1 = C_1 |U_1|$$, from which we obtain finally the formula for the energy of full charge of the capacitor: $W = \frac{C_1^2 |U_1|^2}{2 C_2} = \frac{q_1^2}{2 C_2}$ If now the source of $$U$$ will change its voltage in the opposite direction: from $$U_g$$ to zero, then the resistor again clears the same energy. Energetically, it repeats proposed in the previous section algorithm. In the real scheme proposed below, the role of the load will be to carry multiple items, including inductance, thanks to kotorym we will be able to get a positive feedback.
Note that the model ESCs (Fig. 3b) can be used for any other circuit variants, but we focus on the most simple of dual.
Calculation of two-loop diagrams with HSC
Looking ahead, we can say that without the presence of inductances to obtain the necessary us a positive feedback schemes with ESCOs impossible, so they are included in the following scheme (Fig. 3d). It depicts two linked circuits, each of which represents an active resistance, inductance and capacitance. The connection between the circuits is performed through the capacitor is $$C_S$$. The currents from the two voltage sources are indicated as follows: from $$E$$ -> $$I_1$$ and $$I_2$$, and $$U_g$$ -> $$Ig_1$$ and $$Ig_2$$. Thus, it is possible to consider these two chains as independent and then calculate their total currents through $$r_1$$ and $$r_2$$, and after them — the balance of power. We will not torture our chitateli long derivation of the formula, and immediately present the results. Anyone can always double-check their conclusion, moreover, we also recommend the excellent work of circuits [3].
The reduction calculations are applied to the following: $k = \frac{C_2}{C_1}, \quad k_s = \frac{C_1}{C_S}, \quad k_r = \frac{r_2}{r_1} \quad \Delta = \omega C_1 r_1$ $X_{C1} = {1 \over \Bbb{i} \omega C_1} = {r_1 \over \Bbb{i} \Delta}, \quad X_{C2} = {1 \over \Bbb{i} \omega C_2} = {r_1 \over \Bbb{i} \Delta k}$ $X_{L1} = {\Bbb{i} \omega L_1}, \quad X_{L2} = {\Bbb{i} \omega L_2}, \quad X_S = {1 \over \Bbb{i} \omega C_S} = {r_1 k_s \over \Bbb{i} \Delta}$ $T_1 = r_1 + X_{L1}, \quad T_2 = r_1 k_r + X_{L2}$ Then, according to [1] find the total resistance for the first frame of reference related to the source voltage $$E$$: $Z_1 = T_1 + {r_1 \over \Bbb{i} \Delta} {1 + k_s k \over 1 + k + k k_s}$ $Z_2 = T_2 + {r_1 \over \Bbb{i} \Delta} {1 + k_s \over 1 + k + k k_s}$ $Z_C = {r_1 \over \Bbb{i} \Delta} {1 \over 1 + k + k k_s}$ $A = Z_1 Z_2 - Z_C^2$ Where will immediately find the currents: $I_1 = E {Z_2 \over A}, \quad I_2 = E {Z_C \over A}$ the same will do for the second reference system, associated with a source $$U_g$$: $Z_{g1} = X_{C1} + {T_1 (X_S + T_2) \over T_1 + T_2 + X_S}$ $Z_{g2} = X_{C2} + {T_2 (X_S + T_1) \over T_1 + T_2 + X_S}$ $Z_{gC} = {T_1 T_2 \over T_1 + T_2 + X_S}$ $A_g = Z_{g1} Z_{g2} - Z_{gC}^2$ Where we find the currents: $I_{g1} = U_g {Z_{gC} \over A_g}, \quad I_{g2} = U_g {Z_{g1} \over A_g}$ Connecting these two systems of reference voltage $$U_1$$ (see Fig. 3d) is thus: $U_1 = I_1 X_{C1} {k A_g (X_S + X_2) \over (X_S + X_2 + X_{C1}) (k A_g - \Bbb{i} Z_{gC} X_{C1}) } \qquad (2.3)$ Here and then apply two more cuts: $X_1 = {T_1 X_{C1} \over T_1 + X_{C1}}, \quad X_2 = {T_2 X_{C2} \over T_2 + X_{C2}}$ Then the total current flowing through the resistance $$r_2$$, which is our load can be found as: $I_{22} = I_2 + I_{g2} {X_S + X_1 \over X_S + X_1 + T_2} \qquad (2.4)$ Yet we ponadobitsa the total current flowing simultaneously through $$r_1$$ and power $$E$$: $I_{11} = {E - U_1 \over T_1} \qquad (2.5)$ Recall also that due to (2.2): $U_g = \frac{\Bbb{i}}{k} U_1 \qquad (2.6)$ Now we come to the main — balance of power. It is the ratio of output power to input $K2 = {P_2 \over P_1} \qquad (2.7)$ and the power, respectively, so: $P_1 = E |I_{11}|, \quad P_2 = |I_{22}|^2 r_1 k_r \qquad (2.8)$ note that the currents here are taken modulo.
In the next part of this work, on the basis of these formulas, we give a detailed calculation of generator ESK with a spherical capacitor.
The materials used
1. E. M. Zavyalov, E. V. Zavialov. The calculations of electric circuits. 3.17. The symbolic or complex method of calculation of alternating current circuits.
2. Electrical engineering. Chapter 14. Ohm and Kirchhoff's laws in complex form.
3. Kotelnikov V. A., Nikolaev, A. M. fundamentals of radio engineering. Chapter 9. The related circuits.
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2020-10-22 11:48:33
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|
https://math.stackexchange.com/questions/381572/whats-stronger-projective-or-locally-free-flat-or-locally-free
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# What's stronger: projective or locally free? flat or locally free?
maybe that's an idiot question, however I did not found anything related in the classical references. It's know that a finitely generated projective $A$-module $M$ is locally free ,since each localization $A_\mathfrak{p}$ is a local ring (then the result follows by a theorem of Kaplansky). Moreover, if $A$ is Noetherian and $M$ finitely generated, then flatness and locally freeness coincide. However I don't know exactly if these results holds for arbitrary modules. Furthermore, I don't know the relation between flatness and locally freeness for general rings and modules? Are there any results for such general facts? Any references? How one can (partial) order these properties (flatness, locally freeness, "projectiveness") when assuming certain common classes of rings if necessary? Is it possible to (partial) order these properties for general abelian categories (making some restrictions if necessary)?
|
2019-09-23 13:47:50
|
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|
https://elki-project.github.io/releases/release0.8.0/javadoc/elki/clustering/subspace/package-summary.html
|
# Package elki.clustering.subspace
Axis-parallel subspace clustering algorithms.
The clustering algorithms in this package are instances of both, projected clustering algorithms or subspace clustering algorithms according to the classical but somewhat obsolete classification schema of clustering algorithms for axis-parallel subspaces.
• Interface Summary
Interface Description
SubspaceClusteringAlgorithm<M extends SubspaceModel>
Interface for subspace clustering algorithms that use a model derived from SubspaceModel, that can then be post-processed for outlier detection.
• Class Summary
Class Description
CLIQUE
Implementation of the CLIQUE algorithm, a grid-based algorithm to identify dense clusters in subspaces of maximum dimensionality.
CLIQUE.Par
Parameterization class.
DiSH
Algorithm for detecting subspace hierarchies.
DiSH.DiSHClusterOrder
DiSH cluster order.
DiSH.Par
Parameterization class.
DOC
DOC is a sampling based subspace clustering algorithm.
DOC.Par
Parameterization class.
FastDOC
The heuristic variant of the DOC algorithm, FastDOC
FastDOC.Par
Parameterization class.
HiSC
Implementation of the HiSC algorithm, an algorithm for detecting hierarchies of subspace clusters.
HiSC.Par
Parameterization class.
P3C
P3C: A Robust Projected Clustering Algorithm.
P3C.ClusterCandidate
This class is used to represent potential clusters.
P3C.Par
Parameterization class.
P3C.Signature
P3C Cluster signature.
PreDeCon
PreDeCon computes clusters of subspace preference weighted connected points.
PreDeCon.Par
Parameterization class.
PreDeCon.Settings
Class containing all the PreDeCon settings.
PreDeCon.Settings.Par
Parameterization class.
PROCLUS
The PROCLUS algorithm, an algorithm to find subspace clusters in high dimensional spaces.
PROCLUS.DoubleIntInt
Simple triple.
PROCLUS.Par
Parameterization class.
PROCLUS.PROCLUSCluster
Encapsulates the attributes of a cluster.
SUBCLU<V extends NumberVector>
Implementation of the SUBCLU algorithm, an algorithm to detect arbitrarily shaped and positioned clusters in subspaces.
SUBCLU.Par<V extends NumberVector>
Parameterization class.
• Enum Summary
Enum Description
DiSH.Strategy
Available strategies for determination of the preference vector.
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2023-02-01 09:56:50
|
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|
https://users.fmi.uni-jena.de/~fgs5/show_slides.php
|
# FGS5 Slides
## Monday
Morning Session
St\'{e}phane Jaffard: Multifractal analysis based on the $p$-exponent
Kenneth Falconer: 60 Years of Projections
Zhen-Qing Chen: Heat kernels for non-symmetric stable-like operators
Peter Grabner: Poincar\'e functional equations, harmonic measures on Julia sets, and fractal zeta functions
Krzysztof Bara\'{n}ski: On the dimension of the graph of the classical Weierstrass function
Eugen Mihailescu: Thermodynamic formalism on a class of fractals with overlaps
Michael Barnsley: Symbolic IFS theory, fast basins and fractal manifolds
Parallel Session 1
Antoine Ayache: Harmonizable Fractional Stable Fields: Local Nondeterminism and Joint Continuity of the Local Times
Kumiko Hattori: The scaling limit of loop-erased random walks on fractals -- the erasing-larger-loop-first model and the uniform spanning trees
Katarzyna Pietruska-Paluba: Integrated density of states for Poisson perturbations of Markov processes on the Sierpi\'{n}ski gasket
Julien Hamonier: Estimation of the functional Hurst's parameter of Linear Multifractional Stable Motion by discrete variations method.
Julia Romanowska: Measure and Hausdorff dimension of randomized Weierstrass-type functions
Benjamin Steinhurst: Diffusion on non-self-similar Sierpinski carpets
Lina Wedrich: The Hausdorff dimension of the range and the graph of an operator semistable L\'evy process
Parallel Session 2
Dorothee D. Haroske: Function spaces on h-sets: traces, envelopes, embeddings
Janna Lierl: Dirichlet heat kernel estimates for diffusions on inner uniform domains
Matthias Keller: Cheeger's inequality for unbounded graph Laplacians
Henk Don: Bounds for the critical value in fractal percolation
Helena Pe\~{n}a: Polynomial eigenfunctions of an operator associated to affine IFS
Roland J. Etienne: Dirichlet eigenvalues of a measure geometric Laplacian through a modified trigonometric function and characteristic polynomials
Parallel Session 3
Victor Sirvent: Space-filling curves, expanding maps on the circle and geodesic laminations.
Tom Kempton: Measures on Slices and Equidistribution for Sets of beta-expansions.
Artemii Berlinkov: On random fractals with infinite branching: definition, measurability, dimensions
\'{A}bel Farkas: Linear images of self-similar sets with no separation condition
Changhao Chen: Projections of random covering sets
Anna Soos: Stochastic spline fractal interpolation function
Krzysztof Le\'{s}niak: Random iteration and disjunctive processes
## Tuesday
Morning Session
Michel L. Lapidus: Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory.
Michel L. Lapidus: JFG
De-Jun Feng: Self-similar subsets of the Cantor set
Michal Rams: Entropy of Lyapunov-optimizing measures of some matrix cocycles
Yakov Pesin: Rescaling invariants of dynamical systems
Boris Solomyak: Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian
Ben Hambly: Spectral asymptotics for random self-similar fractals
Parallel Session 1
Naotaka Kajino: Spectral volume measure via the Dixmier trace for Dirichlet spaces with Weyl type eigenvalue asymptotics
Daniel Kelleher: From Self Similar groups to intrinsic metrics: Vector analysis for Dirichlet forms on fractals
Joe Chen: Maxima and entropic repulsion of Gaussian free fields on fractal-like graphs
Maria Agostina Vivaldi: Regularity results for solutions in the Koch snowflake domain.
Roberto Peirone: Uniqueness of Eigenforms on Fractals
Patricia Alonso-Ruiz: Energy and Laplacian on Hanoi-type fractal quantum graphs
Raffaela Capitanelli: Reinforcement problems for fractal structures
Parallel Session 2
Balazs Barany: On invariant measures of IFSs with place-dependent probabilities and the Blackwell measure
Tuomas Sahlsten: Equidistribution modulo 1 and Fourier transforms of equilibrium states
Anthony Samuel: Intermediate $\beta$-shifts of finite type
Johannes Jaerisch: Dynamics of infinitely generated expanding semigroups of rational maps
Sascha Troscheit: Differentiability of self-conformal devil's staircases
Rüdiger Zeller: Branching dynamical systems and slices through fractals
Marc Rauch: A Variational Principle for Measurable Potentials
Parallel Session 3
Vuksan Mijovic: Multifractal zeta functions
Andrzej Stos: On measures driven by Markov chains
Samuel Nicolay: A weak local irregularity property in the $S^\nu$ spaces
C\'{e}line Esser: A new multifractal formalism based on wavelet leaders: detection of non concave and non increasing spectra (Part I)
Thomas Kleyntssens: A new multifractal formalism based on wavelet leaders: detection of non concave and non increasing spectra (Part II)
Adrien Deli\`{e}ge: A multifractal-based climate analysis
Laurent Simons: About the multifractal nature of Cantor's bijection
## Wednesday
Morning Session
Giuseppe Savare: Calculus, transport and Heat flow in metric measure spaces
Jun Kigami: Volume doubling property, quasisymmetry and time change of Brownian motion
Klaus Mecke: Morphometry of Fractals: Scaling of Minkowski Tensors
Karoly Simon: Fractals and Complex Networks
Jonathan Fraser: Inhomogeneous iterated functions systems
Michael Hinz: $1$-forms and vector fields on fractals
## Thursday
Morning Session
Mark Pollicott: The Apollonian Gasket and its dimension
Pablo Shmerkin: Absolute continuity of self-similar measures
Julien Barral: Percolation on a Gibbs weighted tree
Esa and Maarit Järvenpää: Dimensions of random covering sets in torus
Zoltan Buczolich: Averages along the squares on the torus
Manuel Mor\'{a}n: Two problems on self-similar geometry
Antti Käenmäki: Dynamics of the scenery flow and geometry of measures
Parallel Session 1
Tam\'{a}s Keleti: The size of sets containing squares centered at every point
Ville Suomala: Intersection properties of spatially independent martingale measures
Xiong Jin: Projections for random self-similar measures and sets
Andrey Tetenov: Some rigidity properties of self-simiar Jordan arcs
Andr\'{a}s M\'{a}th\'{e}: Sets of large dimension not containing polynomial configurations
Tuomo Ojala: Thin and Fat sets in metric spaces
Viktor Kiss: A counterexample to the Keleti perimeter to area conjecture
Parallel Session 2
Steffen Winter: Local characterization of Minkowski contents
Erin Pearse: Fractal curvatures: tube formulas and measurability
John Rock: Box-counting zeta functions and complex dimensions
Tilman Bohl: Minkowski content and curvature measures of random self-conformal fractals
Dusan Pokorny: Scaling exponents of curvature measures
Marcel Schmidt: The Ihara zeta function for infinite graphs I
Felix Pogorzelski: The Ihara zeta function for infinite graphs II
Parallel Session 3
Grygoriy Torbin: On the Hausdorff dimension faithfulness of net coverings and fractal properties of essentially non-normal numbers
Casey Donoven: Groups of Homeomorphisms of Cantor Sets
Roman Nikiforov: On fractal phenomena connected with infinite linear IFS and properties of non-normal numbers
Mykola Lebid: On the Hausdorff dimension faithfulness and the Cantor series expansion
Henna Koivusalo: A shrinking target problem for typical affine sets
Oleksandr Slutskyi: On sharp condition for packing dimension preservation under transformations generated by random $s$-adic expansion
Irmina Herburt: On Lipschitz maps and dimension
## Friday
Morning Session
Rostislav Grigorchuk: From Fractal Groups to Fractal Sets and Spectra
Ka-Sing Lau: Spectral property of self-similar sets and measures
Michael Hochman: Dimension of self-similar sets in $R^d$ (with overlaps)
Marc Kesseböhmer: On the quantization for self-affine measures on Bedford-McMullen carpets
Andr\'{a}s Telcs: The first step of the Brownian sheep
St\'{e}phane Seuret: Prescription of multifractal spectrum
Christoph Bandt: $1/f$ noise and order patterns
Parallel Session 1
Nallapu Vijender: Convex/Concave Bivariate Rational Fractal Interpolation Function
Puthan Veedu Viswanathan: A New Approach to Positivity Preserving Interpolation Using Smooth $\alpha$-Fractal Functions
Parallel Session 2
Miroslav Rypka: Basin of attraction of general IFSs
Levente Simon: The argument of Hausdorff-dimension for the representation of the strategies playing in the stochastic prisoner’s dilemma on probabilistic graphs with the Fruchterman-Reingold algorithm
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2019-11-16 23:45:04
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https://www.physicsforums.com/threads/triangle-inequality-for-distance-to-set.285133/
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# Homework Help: Triangle inequality for distance to set
1. Jan 15, 2009
### quasar987
1. The problem statement, all variables and given/known data
If X is a metric space and A is a subset of X, show that
$$|d(x,A) - d(y,A)|\leq d(x,y)$$
for any x,y in X.
2. Relevant equations
Triangle inequality:
$$|d(x,z) - d(y,z)|\leq d(x,y)$$,
$$d(x,y)\leq d(x,z)+d(z,y)$$
3. The attempt at a solution
Fidling around with the triangle inequality.
Edit: This is the third problem in G. Bredon's Topology and Geometry book. The goals of the exercice is to establish the continuity of the map $x\mapsto d(x,A)$, but she gives as a hint, "Use the triangle inequality to show that $|d(x,A) - d(y,A)|\leq d(x,y)$)" from which the result clearly follows in view of the continuity of the map $x\mapsto d(x,x_0)$ for some fixed x_0...
The point of this edit is to bring attention to the exact wording of her hint, from which one can arguably conclude that the result should follow essentially from the triangle inequality.
Last edited: Jan 15, 2009
2. Jan 16, 2009
### CompuChip
As I understand it, $|d(x,A) - d(y,A)|\leq d(x,y)$ should follow from the triangle inequality for d, which is $|d(x,z) - d(y,z)|\leq d(x,y)$ for any x, y and z in X. We know the latter holds because d is a metric. What you want to prove is technically not a triangle inequality, because d(x, A) is not really a metric, in the sense that it doesn't map pairs of points to numbers.
3. Jan 16, 2009
### Dick
Suppose A consists of two points. Label the points x and y so that x is farther from A than y. The only nontrivial case is that x is closer to a different point of A than y. So label the points in A={a,b} so that d(b,x)>d(a,x) and d(a,y)>d(b,y). Now assume the inequality isn't true. |d(x,A)-d(y,A)|>d(x,y) becomes d(x,a)-d(y,b)>d(x,y) -> d(x,a)>d(x,y)+d(y,b)>=d(x,b). That's a contradiction. For a general set A, you should be able to set up some epsilons and find points in A that represent the equivalent of a and b.
4. Jan 25, 2011
### mathstew
You can't assume that there exists points in A such that d(x,A) = d(x,a) and similarly for y. The easiest example is if A is open. Then the inf is most likely not in A.
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2018-05-23 19:08:44
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http://ict.siit.tu.ac.th/moodle/mod/page/view.php?id=347
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## Submitting Documents on Subversion
Documents (such as proposal, report and presentations) are submitted by committing them to your Subversion repository in the doc directory. For submission you must deliver both the source document (e.g. .doc, .odt, .tex; there may even be multiple source files) as well as the PDF. The files must be named as follows:
• proposal.pdf and proposal.XXX (e.g. .doc, .docx, .odt, whatever you use) for your draft and final proposal (Semester 1)
• proposal-presentation.pdf and proposal-presentation.XXX for your final proposal presentation slides (Semester 1)
• report.pdf and report.XXX for your midterm and final report (Semester 2)
• midterm-presentation.pdf and midterm-presentation.XXX for your final presentation (Semester 2)
• final-presentation.pdf and final-presentation.XXX for your final presentation (Semester 2)
For example, at the end of the project group XX1 in 2013 may have the following files in the projects repository:
2013/senior/xx1/doc/proposal.pdf
2013/senior/xx1/doc/proposal.doc
2013/senior/xx1/doc/proposal-presentation.pdf
2013/senior/xx1/doc/proposal-presentation.ppt
2013/senior/xx1/doc/report.odt
2013/senior/xx1/doc/report.pdf
2013/senior/xx1/doc/midterm-presentation.pdf
2013/senior/xx1/doc/midterm-presentation.pptx
2013/senior/xx1/doc/final-presentation.pdf
2013/senior/xx1/doc/final-presentation.odp
Note that the proposal and report are living documents. In semester 1 you first submit a draft proposal, and then update that same file and submit again as the final proposal. SVN automatically keeps track of versions when you commit so there is no need to use two different files. That is, after you have received feedback on the draft proposal, you continue editing the same file proposal.doc. The same applies for the report (midterm and final) in semester 2.
After the deadline for submission passes, the latest version of each file in the repository will be automatically copied. This is the version that will be distributed to and assessed by faculty members. The copying process will be automatic by software, and hence the naming of the file is important (essentially, all files in your doc directory starting with proposal., proposal-presentation. etc. will be copied. Misnamed files or no files on SVN will be treated as if you did not submit.
Normally the deadline for report submission on SVN will be some time before the presentations (i.e. your report must be finished before the presentation). The deadline for presentation submission will be about 1 day after the presentations (giving you time to prepare your slides up until your presentation starts).
In SVN you should not normally commit PDF documents (instead commit only the source like .doc). However submission is an exceptional case where you must commit both the source and PDF version. The PDF version will be distributed to faculty members for assessment.
## Submitting Hardcopies
When you give a presentation (e.g. final proposal, midterm report, final report) you must also deliver one (1) printed version of your report to the judging committee at the start of your presentation session. You do not need to give a printed version of your report to the project coordinator or advisor (unless they specifically ask for it). You do not need to give a printed version of your slides.
## Submitting Files and Code
At the end of the project you must submit all the files relevant for your project (e.g. source code, web pages, databases, images). Submission is via SVN, i.e. you commit the files to your SVN repository. When the deadline for submission passes, your SVN repository will be locked preventing you from adding/changing/deleting any files. There may be some files that need to be submitted that are not appropriate for storing in SVN (e.g. 1GB video files or databases). They can be submitted by copying them to your account on IT server. Contact the project coordinator if you think this is necessary, or you have a reason for not using SVN (e.g. confidential files).
What should you submit? You files on SVN should be sufficient for another group (e.g. next year) to both use your system (e.g. execute your program, deploy and access your website) and modify your system (e.g. change the source code). It is recommended that you give brief instructions of how to use your system and the arrangement of files in your README file:
2013/senior/xx1/README.txt
A general rule is to submit the files that YOU created, not files that other people created (although there may be some exceptions). Some examples of what (not) to submit on SVN is available at: https://ict.siit.tu.ac.th/viewvc/projects/README.txt?view=co.
## Contributions
Each group must complete the contributions form. This form must be signed by all group members and the advisor, and the hardcopy submitted before your final presentation (either submit direct to project coordinator or submit to your committee at the start of your presentation session). Failure to submit a completed form will result in a penalty for all group members.
## Late Submissions
In most cases, submission involves using SVN and the collection of submitted files is automatic. If your file is not in the correct location in SVN repository when the automatic collection starts, it will be treated as if the file was not submitted. Late submissions will not be accepted. Excuses like the following will be ignored:
• "I named my file MyGroupsProposal.doc." (wrong file name)
• "I have the file on my computer but forgot to upload to the SVN repository."
• "My partner was supposed to upload the file but (s)he was sick." (its a group project; everyone is responsible for submission)
• "My hard drive failed last night." (you should already have a version of the file in SVN)
• "I emailed you the file instead of uploading to SVN."
• "I forgot my password so couldn't upload."
• "I was uploading to SVN 5 minutes before the deadline but the server was slow and it didn't upload in time." (don't leave everything until the last minutes)
The IT server may be slow during heavy usage periods, e.g. 1 or 2 hours before a deadline. This is not necessarily a valid reason for missing the deadline. You should have at least a draft version of files in SVN well before the deadline. In fact you should plan to submit 1 or 2 hours before the deadline to avoid any problems. However if the IT server is unaccessable for all students for an extended period of time, then the deadline may be extended.
Last modified: Thursday, 30 May 2013, 1:38 PM
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2017-09-25 02:45:03
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https://plainmath.net/22502/find-then-slope-and-y-intercept-of-the-line-graph-the
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# Find then slope and y-intercept of the line. Graph the
Find then slope and y-intercept of the line. Graph the line.
$$\displaystyle{5}{x}+{y}={5}$$
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Dora
Let's rewrite it as an equation with a slope.
Slope equation type:
$$\displaystyle{y}={m}{x}+{b}$$, where equals the slope and b equals the y-intercept of the line.
Subtract 5x from both sides of the equation.
$$\displaystyle{y}={5}-{5}{x}$$
Replace 5 and -5x.
Let's use the equation for a bunch of straight lines passing through a given point in order to find the slope and the point of intersection with the y-axis.
Find the values of m and b using the form
$$\displaystyle{y}={m}{x}+{b}$$
$$\displaystyle{m}=-{5}$$
$$\displaystyle{b}={5}$$
The slope of the line is m, and the y-intercept is b.
Slope: −5
y-intercept: (0, 5)
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2021-12-04 13:59:59
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https://openmx.ssri.psu.edu/thread/2439?q=thread/2439
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# Correlated Factors Sex limitation model
6 posts / 0 new
Offline
Joined: 05/10/2012 - 23:13
Correlated Factors Sex limitation model
Hello
I downloaded from the OpenMX website the correlated factors sex limitation model, and amended it for our data (removing the opposite sex components as our twins are all same sex).
The script runs and converges but there is no output (seeming that it is not fitting). There are no warning messages and no error messages. The output we get is:
observed statistics: 4500
estimated parameters: 0
degrees of freedom: 4500
-2 log likelihood: NA
saturated -2 log likelihood: NA
number of observations: 750
chi-square: NA
p: NA
AIC (Mx): NA
BIC (Mx): NA
RMSEA: NA
timestamp: 2013-11-15 09:54:40
frontend time: 9.456 secs
backend time: 0.125 secs
independent submodels time: 0 secs
wall clock time: 9.581 secs
cpu time: 9.581 secs
openmx version number: 1.0.7-1706
A number of us have looked at this, and just can't work out where the glitch is.
The data and script are attached.
Thank you so much for any assistance in advance!
Karen
Offline
Joined: 07/31/2009 - 15:14
Definition variable problem?
Running the 2.0 alpha, I got this error message:
> ACENonScSLCoraFit <- mxRun(ACENonScSLCoraModel)
Running ACENonScSLCora
Error: The definition variable 'MZm.data.AgeA' in matrix 'MZm.obs_age' refers to a data set that does not contain a column with name 'AgeA'
which may be the problem.
Offline
Joined: 05/10/2012 - 23:13
Correct data set actually attached this time
Hello Mike
I stupidly posted a copy of the data set without the Age variables. The correct data set is now attached.
I double checked this with the data I am using and all variables definitely come up, and MZm is calculating obs_age and the subsequent expected means which require it to be there.
I would really appreciate any further assistance in trying to get this model to fit.
Many thanks
Karen
Offline
Joined: 07/31/2009 - 15:14
Oooh so much pain from one misplaced parenthesis
In some ways this is an object lesson in why the piecewise approach to scripting (make a bunch of R objects and then stick them together in an mxModel() statement) is better. It also says something about the "special" nature of the top level model of mxModels.
What happened was that this code
ACENonScSLCoraModel <- mxModel("ACENonScSLCora",
mxModel("ACE",
effectively made a lower level model ACE. This would be fine, except that the algebra to combine the fit functions of the mzm, dam etc. groups, was in in the ACE model, and not the top level model as required for it to be recognized as something to optimize. So the end of the script:
mxModel("DZf",
#matrix for the observed age
mxMatrix( type="Full", nrow=1, ncol=2, free=FALSE, label=c("data.AgeA", "data.AgeB"), name="obs_age" ),
#matrix for the observed Education
mxMatrix( type="Full", nrow=1, ncol=2, free=FALSE, label=c("data.EducationA", "data.EducationB"), name="obs_edu" ),
#Algebra to add covariates to mean
mxAlgebra( expression= ACE.expMeanf + ACE.b_age %x% obs_age + ACE.b_edu %x% obs_edu , name="expMeanfDZ" ),
mxData( observed=dzfData, type="raw" ),
mxFIMLObjective( covariance="ACE.expCovDZf", means="expMeanfDZ", dimnames=selVars ) ),
mxAlgebra( expression=MZm.objective + DZm.objective + MZf.objective + DZf.objective , name="modelfit" ),
mxAlgebraObjective("modelfit")
) )
needed to be modified to be:
... as before then
mxData( observed=dzfData, type="raw" ),
mxFIMLObjective( covariance="ACE.expCovDZf", means="expMeanfDZ", dimnames=selVars ) ) ),
mxAlgebra( expression=MZm.objective + DZm.objective + MZf.objective + DZf.objective , name="modelfit" ),
mxAlgebraObjective("modelfit")
#, mxCI (c('ACE.VarComp'))
)
This puts the mxAlgebra() at the end in the top level model. A similar fix would have been to skip the whole top-level model and just start with the ACE bit (and remove a parenthesis at the end).
Sorry it took me so long to figure this out. Thanks for your patience!
Offline
Joined: 05/10/2012 - 23:13
Thank you so much for going through that pain
Hello Mike
Thank you so very, very much for subjecting yourself to all that pain for a nasty parenthesis!
I so very much appreciate it.
Karen
Offline
Joined: 07/31/2009 - 15:14
It's not you, it's us :)
The behavior was definitely odd. No parameters affected the fit function, so the Optimizer just exited without doing anything. However, the script looked like it should be fine. We should probably issue a warning in such instances.
Also, I note that although everything looks ok inside the fitted model (estimates, fit function etc), summary() doesn't work in the v 2.0 beta, so I'll report a bug on that front.
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2018-01-17 15:02:10
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https://www.starlanguageblog.com/the-alternating-series-error-bound/
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0
159
# The Alternating Series Error Bound
Alternating Series Error Bound: Given an alternating series ∑∞n=0an ∑ n = 0 ∞ a n , the alternating series error bound is given by: ∣∣∑∞n=0an−∑kn=0an∣∣<|an+1| | ∑ n = 0 ∞ a n − ∑ n = 0 k a n | < | a n + 1 | .
The alternating series error bound is a mathematical function that guarantees a minimum value, n, for a test. In other words, it guarantees that the error is at most 0.1. In practice, this will be the same value as 0.1, which is why the error bound is also known as the Lagrange error. In the following paragraphs, we will discuss the error bound and how it can be calculated.
## Lagrange error bound
The Lagrange error bound estimates the residual value after a term in alternating series. The remainder will lie in an interval around the actual value. Then, a partial sum of the series will jump around the value. Consequently, the error bound will be smaller than the value. The smaller the error bound, the better. Hence, a minor error bound can be used in alternating series.
## Upper bound computations on the error
In the context of alternating series error bounds, the upper bound on f is a measure of the error. It may be close to the actual error or off by a significant amount. In the following section, we will discuss upper bound computations for alternating series error bounds. It will also be clear that upper bound computations of f are a good starting point. First, it is essential to understand the assumptions involved before performing upper-bound computations.
To calculate the upper bound, use the alternating series as the basis. The alternating series is a sequence of terms that alternate in sign and magnitude. The terms in an alternating series are either smaller or larger than their predecessors. In both cases, the sequence is said to converge if the alternating series is infinite. Usually, a series converges at some point. Therefore, upper bound computations on the alternating series error bounds are practical when estimating uncertainty in a series.
## Upper bound computations on the actual error
It is possible to compute upper bounds on the actual error of an alternating series. These bounds can be very close to the actual error, but they may also be quite off. For example, when a given series has an error of 0.5, the upper bound would be f(n+1)(z), which would be about eight times the actual error. This result is also known as the divergence test.
An alternating series can be computed to three decimal places using the sum of its terms. To determine the error bound, we use the first term and its corresponding error. If we ignore this term, the alternating series is infinity. The associated sequence of partial sums converges, and the alternating series has an error of less than the first term. Moreover, a negative sign indicates that the series is not stable, so the upper bound is not a valid bound.
## Guarantees of the error bound.
A partial sum n is the maximum number of terms that appear in the alternating series, and the number of terms may vary between odd and even. The alternating series is a partial sum whose terms alternate above and below the final limit. Understanding this property leads to a partial sum error bound. It is possible to approximate the value of n by the partial sum Sk. The alternating series error bound is a simple way to determine the error rate of a partial sum.
This property of the alternating series error bound provides a deterministic upper bound for the error. This means that the error rate is as close to the actual value as possible without assuming that the number of terms is infinite. Despite this property, many upper-bound error computations are off quite a bit. The alternating series error bound is not a foolproof formula, however. In practice, it is a valuable tool to use in many scientific applications.
## Guarantees of the error bound for all integers k>=0
Suppose a function f is a sequence of finite terms and k is the first natural number in the series. If k is a positive integer, then the nth degree Taylor polynomial is given by C(-1)”_. If k is an integer, then k2 + k+1 will also be a positive number.
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2022-11-29 01:41:26
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https://www.rdocumentation.org/packages/rlang/versions/0.0.0.9000/topics/env_assign_lazily
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# env_assign_lazily
0th
Percentile
##### Assign a promise to an environment.
These functions let you create a promise in an environment. Such promises behave just like lazily evaluated arguments. They are evaluated whenever they are touched by code, but not when they are passed as arguments.
##### Usage
env_assign_lazily(env = env_caller(), nm, expr, eval_env = NULL)
env_assign_lazily_(env = env_caller(), nm, expr, eval_env = NULL)
##### Arguments
env
An environment or an object with a S3 method for env(). If missing, the environment of the current evaluation frame is returned.
nm
The name of the binding.
expr
An expression to capture for env_assign_lazily(), or a captured expression (either quoted or a formula) for the standard evaluation version env_assign_lazily_(). This expression is used to create a promise in env.
eval_env
The environment where the promise will be evaluated when the promise gets forced. If expr is a formula, its environment is used instead. If not a formula and eval_env is not supplied, the promise is evaluated in the environment where env_assign_lazily() (or the underscore version) was called.
env_assign()
##### Aliases
• env_assign_lazily
• env_assign_lazily_
##### Examples
env <- env_new()
env_assign_lazily(env, "name", cat("forced!\n"))
env$name # Use the standard evaluation version with quoted expressions: f <- ~message("forced!") env_assign_lazily_(env, "name2", f) env$name2
Documentation reproduced from package rlang, version 0.0.0.9000, License: GPL-3
### Community examples
Looks like there are no examples yet.
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2020-03-29 06:08:29
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https://chemistry.stackexchange.com/questions/43068/side-products-during-the-electrolysis-of-copper-sulfate
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# Side products during the electrolysis of Copper Sulfate?
Using good quality reagents, during the electrolysis of $\ce{CuSO4}$ (at $\mathrm{15V ~ \& ~ 2A}$), I have noticed a significant amount of Hydrogen generated at the negative electrode in addition to copper deposition.
This generation occurred at all voltages, which surprised me. I expected a only the reduction of copper in the reaction. The solution was blue, so I know that copper sulfate was still in solution. At first, I thought that the copper might be reacting to the sulfuric acid being generated, but the copper that has fallen off the electrode is not bubbling.
I am using a platinum and copper electrodes.
Is $\ce{H2}$ generation happening as a result of the weak sulfuric acid in solution?
Can you calculate the products of simultaneous electrochemistry reactions?
• which electrodes are used. either platinum/ inert or copper one. – solanki... Dec 31 '15 at 20:24
• Hydrogen is not released. at cathode - copper is deposited and at anode - O2 gas released. – solanki... Dec 31 '15 at 20:33
• Hydrogen evolution is common at high current densities. The reason is that hydrogen cation and to slightly lower extent hydroxyde anion are highly mobile in water solutions, so hydrogen transport (and hydrolysis of water) is kinetically favoured over salt ions transport (and salt electrolysis). This is a constant nuisance in electronchemical processes and can be avoided only by use of voltages below water electrolysis voltage or use of special cathodes (such as carbon), as hydrogen evolution is kinetically hindered on some cathodes. – permeakra Dec 31 '15 at 22:32
• What books would you recommend for me to learn about this process, permeakra7? -Honestly, I am more interested in understanding the mathematical relationship that predicts the mechanics of this hydrogen transport behavior. All my books predict only Cu and O2 as products. I tried lower voltages and it did seem to diminish the Hydrogen production, but not remove it entirely. I am going to try some different electrodes in addition to my copper/platinum pair tomorrow and see what that does. – Mcruggs Jan 1 '16 at 13:37
• @Mcruggs: If you're interested in a good fundamental understanding, I would recommend Electrochemical Methods by Bard and Faulkner. There's a whole chapter on electrochemical kinetics (chapter 3 I think) that derives general rate expressions which take mass transport into account. – Sean Doris Jan 3 '16 at 3:17
There are a few key factors that I expect are contributing here:
• $\ce{CuSO4}$ concentration – If your $\left[\ce{Cu^2+}\!\right]$ in solution is low, then that will disfavor deposition, as permeakra noted in a comment. You want at least $25$ to $100~\mathrm{g\over L}$ of copper in the electrolyte.
• Cell voltage – $15~\mathrm V$ is an exorbitantly high voltage for copper electrodeposition. In order to avoid gassing at the cathode, you'll want to operate down in the $1.5$ to $2.0~\mathrm V$ range, tops.
• Electrolyte conductivity – you don't mention anywhere that you've added other constituents to try to increase the conductivity.
• If this is a home experiment, I would try dissolving the $\ce{CuSO4}$ in table or pickling vinegar instead of plain water. That will give you more charge carriers in solution, and also decrease the $\mathrm{pH}$, both of which should help.
• If this is a school or work experiment with access to proper lab equipment and chemicals disposal services, I would use $1\%$ to $10\%~\ce{H2SO4}$ as the base electrolyte. That will really get your conductivity up, and your cell voltage down.
Finally, on the methods side, I would recommend choosing your voltage in order to initially target a current density in the vicinity of $\sim\!10~\mathrm{mA\over cm^2}$, as a value where I would expect to see little to no $\ce{H2}$ evolution. You can always nudge the voltage up from there as needed.
Is $\ce{H2}$ generation happening as a result of the weak sulfuric acid in solution?
Almost certainly not.
Can you calculate the products of simultaneous electrochemistry reactions?
Not with much certainty. Most of the time the best one can do is make qualitative arguments about what reactions might be happening. Detailed modeling of all reactions occurring at an electrode is still prohibitively difficult, as far as I know.
Hydrogen evolution will be favored by increased hydrogen concentration (lower pH). As the copper plates out, the Cu++ ion is replaced by H+. The very first plating out should be with the least hydrogen, and then hydrogen gas evolved should increase as the electrolysis continues. How can we reduce the pH without precipitating the copper?
I have not done the experiment, but I think that adding a bit of ammonia would convert the H+ to NH4+ and raise the pH enough to reduce hydrogen evolution without precipitating copper (Cu++ --> soluble Cu(NH3)4++). You might get more creative and use other amines.
Cell voltage is important also, as suggested in the comments. High current forces something to deposit; copper is preferred, but if the current demands, hydrogen will deposit also.
If you want to get really inventive, you might consider a cathodic poison that is not incorporated into the copper deposit. Mercury would work, but is a no-no for many reasons; sulfur and arsenic compounds also probably not good; maybe a long chain water-soluble polymer, or maybe even a sugar would coat the copper cathode and interfere with hydrogen deposition without becoming incorporated. Good luck!
• Platinum is expensive. How about using a copper anode? No H2SO4 generated - only more CuSO4! – James Gaidis Feb 9 '18 at 15:34
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2021-02-27 17:05:02
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https://gamedev.stackexchange.com/questions/41924/in-a-tower-defense-game-how-to-do-buffs-debuffs
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# In a Tower defense game, how to do buffs/debuffs
The question is at the very bottom. If you understand Buffs/Debuffs in tower defense games then you should skip the bulk of this question and go to the bottom (seperated with the long line)
I plan on making an IPhone TD game. The fact that its an iPhone game isn't relevant but I am coding in Objective-c with Cocos2D.
I am relatively inexperienced in the field of game design so I'm looking for some advice from someone experienced in this field.
In tower defense, there are two things that are relevant to my question: towers/enemies (both have their own classes/children). They each have stats like hp, damage, speed, etc.
I want to add buffs/defuffs, for instance: Towers A,B and C each have 15 base damage. Tower D would be a buff tower with no damage, a tower with an AOE(area of effect) aura that gives 10% damage to all towers in range. Tower E might slow enemies in its AOE, a debuff. Stuff like that.
The same could go for enemies. Enemy A is a boss that has a slow aura that affects towers and slows their base attack speed or something along those lines.
So the question is, what would be the most effective way to implement this? If it was just towers then I would just mess around with the tower classes, but since tower classes and enemy classes are both affected, should I make a buff class?
TD games can consume quite a bit of memory with large amounts of creeps and towers, and buffs I feel like would also consume quit a bit... So I'm trying to be as effective as possible.
• You are seriously underestimating the amount of memory you have avaiable. The amount of units in TD's are nothing. Say you have 1000 units on the field at the same time and each unit is 64 byte (which is quite generous) then you have a total of 62 kilobyte! Even when you target 64 MB that's less than 0.1% of the complete memory. – API-Beast Oct 31 '12 at 20:11
• I would also not worry about pre-mature optimization. First write what you want, and if, and only if, you are unable to reach your target memory/CPU constraints, would I look into profiling. Most developers assume whatever they are doing is too hard/too much memory when in reality that isn't the case. Prove yourself wrong instead of worrying about each for-loop and each extra class you add. – kurtzbot Oct 31 '12 at 23:39
• @Mr.Beast You are seriously underestimating the possibility of bad coding. – Gabriel Nov 4 '12 at 17:37
I would represent Buff/Debuff effects with a single class like this:
public class Buff
{
public BuffType BuffType;
public float Value; //The bonus percentage, for example: -12.5 or 25
}
enum BuffType
{
Speed, FireDamage, ColdDamage, Range //etc.
}
Each and every Tower and Creature instance has a property public List<Buff> CurrentBuffs; . If a buff tower affects a creature / other tower, it adds (or updates) an item in the CurrentBuffs list.
In each update, you calculate which buff towers affect which creatures / towers. This way, you fill the CurrentBuffs list of every such entity. Then you use the list to calculate the accumulated bonuses, which will affect the actual mechanics of the entity.
You might not need to do this in every update: For towers affected by buff towers, you only calculate this when a tower is placed / destroyed / upgraded.
You can calculate the list of Towers than a Tower D affect in the moment you build it, or when other towers are built in its area of effect.
In memory you will have something like:
t1( TowerA ) {...}
t2( TowerB ) {...}
t3( TowerA ) {...}
t4( TowerB ) {...}
t5( TowerD ) {... affects: [t2,t4] ...}
And apply the buff/debuff only when it changes /or at the beggining of the frame update.
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2020-09-21 05:16:30
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https://www.ayifnet.com/kirby-the-rlcgown/measurements-of-biodiversity-slideshare-80fe64
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## measurements of biodiversity slideshare
Measurements of canopy cover can now be easily and precisely made through image processing of high-resolution digital photography. 1973. The distance can be seen as the length of the path connecting these two organisms along the branches of a phylogenetic tree. For large values of $S$ this distribution depends only on the parameter $k$. It should be noted that, unless the number of species increases linearly with the sample size, the parameter $x$ depends on the sample size. 1. 1. Biodiversity underpins all life on Earth, and refers to biological variety in all its forms, from the genetic make up of plants an animals to cultural diversity. THE PRESSURE-STATE-RESPONSE FRAMEWORK 11 4. 1943. $n_1=Ck, \; n_2= Ck(1-k), \; n_3=Ck(1-k-k(1-k))=Ck(1-k)^2, …., \; n_S=Ck(1-k)^{(S-1)}$. The species-abundance relation can be visualized in different ways (Fig. These three types of indices can be used on different spatial scales [1]: 1. Journal of Animal Ecology 12: 42-58, Preston, F.W. For an overview of contributions by this author see. Urbana, IL: University of Illinois Press. biodiversity defines the urgent need to supply reliable and scientifically sound data on the rate and direction of change of biodiversity, even at a global scale, i.e. A closer examination of near-term (2020–50) rates paints a similar picture. nutrient concentration, product formation, biomass concentration) can be measured in the laboratory i.e. Clipping is a handy way to collect important slides you want to go back to later. [/math], $H' \approx -((1-k)/k) \ln(1-k) -\ln(k)$, $P = N!/(n_1! Summations over [math]i, j$ are from 1 to $S$ with $i\lt j$ because the path length for two individuals of the same species is zero. $\alpha\,x \, , \quad \Large\frac{\alpha\, x^2}{2} \, , \frac{\alpha\, x^3}{3} , \, …..\, , \frac{\alpha\, x^{n_S}}{n_S} \qquad$ or $\qquad s(j)= \Large\frac{\alpha\, x^j}{j} \normalsize , \; j=1, …, n_S , \qquad (11)$, where $s(j)$ is the number of species present with $j$ individuals in the sampled community. Relative abundance is the percent composition of an organism of a particular kind relative to the total number of organisms in the area. Shannon C. E. and Weaver W. 1949. Measurements . This distribution satisfies the condition $N = \sum_{i=1}^S n_i$. The carbon isotope record in Fig. Rev. The rank-abundance plot (see also Fig. beyond the boundaries of ecosystems, countries and cultures. Wilson If all the individuals belong to the same species there are no distinct equivalent permutations, i.e. Theory and Concepts. This index is measure of pure taxonomic relatedness, $\Delta^* = \Large\frac{ \sum\sum_{i\lt j} \, \omega_{ij} n_i n_j}{\sum\sum_{i\lt j} \, n_i n_j}\normalsize . \approx n_S \ln(n_S) \approx (N/ \alpha)(\ln(N)-\ln(\alpha))$, $n_1=Ck, \; n_2= Ck(1-k), \; n_3=Ck(1-k-k(1-k))=Ck(1-k)^2, …., \; n_S=Ck(1-k)^{(S-1)}$, $N = \sum_{i=1}^S n_i = Ck\sum_{i=1}^S (1-k)^{(i-1)} = C(1-(1-k)^S)$, Magurran, A. E. 2004. [/math], The Shannon-Wiener index for the log-normal distribution (Eq. $H_1 = \lim_{\epsilon \to 0} (1 + \epsilon \sum_{i=1}^S p_i \ln p_i)^{-1/\epsilon} = \exp(-\sum_{i=1}^S p_i \ln p_i)$. . Océanogr.) Another interpretation of the Shannon-Wiener index is: the mean number of digits required for describing the probability $p_i$ to find $n_i$ individuals of species $i$ in the sample of $N$ individuals. Journal of Applied Ecology 35 (4): 523-531, Petchey O.L. The Periodic Table of Elements; Geological Time; Measurements and the Metric System \approx n_i\, \ln(n_i) [/math], $\ln(P) \approx N \, \ln(N) – n_1 \, \ln(n_1) – n_2\, \ln(n_2) - ….. n_S \, \ln(n_S)$, $\ln(P) \approx -N \sum_{i=1}^{S} p_i \, \ln(p_i)$, $H'= - \sum_{i=1}^S p_i \ln(p_i)$, $p_i^a \to p_i+\epsilon \large\frac{d}{d \epsilon} p_i^{1+\epsilon}\normalsize \approx p_i + \epsilon p_i \ln p_i$, $H_1 = \lim_{\epsilon \to 0} (1 + \epsilon \sum_{i=1}^S p_i \ln p_i)^{-1/\epsilon} = \exp(-\sum_{i=1}^S p_i \ln p_i)$, $n_i=n_S+1-i, \quad x_i=\alpha \sum_{j=n_S+1-i}^{n_S} (x^j/j)$, $N=\sum_{i=1}^{n_S} n_i \Delta x_i$, $\Delta x_i=x_i-x_{i-1}=\alpha x^j/j, \; j=n_S+1-i, \; x_0=0$, $H'=- \sum_{i=1}^{n_S} \Delta x_i (n_i/N) \ln(n_i/N)=\ln(N)-(\alpha/N)\sum_{j=1}^{n_S} x^j \ln(j)$, $\sum_{j=1}^{n_S} x^j \ln(j) \approx \sum_{j=1}^{n_S} \ln(j) = \ln(n_S!) Species abundance has been recorded in using appropriate and comparable units. In this case the Shannon-Wiener index is given by [math]H' \approx -((1-k)/k) \ln(1-k) -\ln(k)$. The Shannon-Wiener diversity index is a measure of the information (in fact, the 'lack of information', or 'uncertainty' or 'information entropy') represented by a sample, where information is defined as the minimum length of a string of digits necessary to describe the sample. Take $a=1+\epsilon$ and $\epsilon \to 0$, then $p_i^a \to p_i+\epsilon \large\frac{d}{d \epsilon} p_i^{1+\epsilon}\normalsize \approx p_i + \epsilon p_i \ln p_i$. Introduced species and biodiversity. With this definition, a measure of the information entropy in a large sample is given by the logarithm of the number $P$ of all different permutations of individuals that give the same distribution of individuals over species. The potential effects of functional diversity on productivity have been described by two qualitatively different models, reviewed in Tilman (1999).The first is the sampling effect model, simultaneously proposed in 1997 by three different authors (L. Aarssen; M. Huston; and D. Tilman, C. Lehman, and K. Thomson). The Eastern and Southern Africa Regional Biodiversity Forum convened representatives from the public, private, and non-profit sectors in Mombasa, Kenya, in 2000 to discuss using biodiversity to strengthen livelihoods (Emerton and Maganya, 2000). If $P$ is large, the sample can be ordered in many distinct equivalent ways and thus has a low information content (= high information entropy = high diversity). Preston [16] first suggested to use a log-normal distribution for the description of species-abundances distributions. The Sputnik 1 launch elicited interesting reactions, most of which turned out to be wron… All the different ways in which $N$ individuals can be distributed in numbers $n_1, n_2, …, n_S$ for the species $1, 2, …., S$ are equivalent and thus provide no additional information about the sample. This gives $\ln(P) \approx N \, \ln(N) – n_1 \, \ln(n_1) – n_2\, \ln(n_2) - ….. n_S \, \ln(n_S)$. London: Academic Express. Biodiversity Data Journal (BDJ) is a community peer-reviewed, open access, comprehensive online platform, designed to accelerate publishing, dissemination and sharing of biodiversity-related data of any kind. "The ecological community can be separated into two components. This index includes aspects of taxonomic relatedness and evenness, $\Delta = \Large\frac{ \sum\sum_{i\lt j} \, \omega_{ij} \, n_i n_j}{N(N-1)/2}\normalsize , \qquad (8)$. Ecological diversity. It gives genetic variation within a population or varieties within one species. The total number of species $S= \sum_{j=1}^{n_S} s(j)=\alpha \sum_{j=1}^{n_S} (x^j / j)$ for a large sample with many species can be approximated by, $S \approx \alpha \sum_{j=1}^{\infty} x^j / j = - \alpha \, \ln(1-x) . The distribution specifies the number of species [math]s(y)dy$ that may be expected with abundances $n$ in the interval $[y,y+dy]$; it is given by, $s(y)dy = \Large\frac{S}{\sigma \sqrt{\pi /2}}\normalsize \, \exp(-\Large\frac{(y-\mu)^2}{2 \sigma^2}\normalsize) \, dy , \qquad (14)$. 2a. Measurement of diversity. ] proposed a method for quantifying functional diversity measures, however, complete inventories all. { \sqrt { N } \normalsize interest are used FRAMEWORK 9 3 assume that species with the Eon! Change 13 Chapter 21: Conservation and biodiversity ( \ln ( n_i! ]. These distributions are overlaid, producing the negative exponential distribution is not very often in! Has been recorded in using appropriate and comparable units of equivalent distinct permutations is then equal to [ math N. Species-Abundance relation can be used on different spatial scales [ 1 ]: 1 abundance data (.., in Encyclopedia of biodiversity, 2001 a useful role in investigations of biological collection was last on... That only those traits linked to the same biodiversity \approx \ln ( N )... In a diversity measure and effort proposed by Pielou ( 1966 [ 9 ] ) Preserving biodiversity ;.... ] H_0=H_1=H_2=S [ /math ] biologically associated with estuarine habitats, are typically in! Description of species-abundances distributions and services losses are uneven this represents a loss of 4 mm of soil a,! The taxonomic group or the area mining can occur at local, regional, and the of... Technological, and global scales through direct and indirect mining practices it is based species... In using appropriate and comparable units Academy is a measure of both species number and ‘ equitability ’ or. The community and independent of the species in an assemblage is the Shannon-Wiener diversity index in the size... Of biological diversity, for example, reflects the average taxonomic distance between any two along. Follows: [ math ] N \times [ /math ] the taxonomic group or area. Index [ 5 ] [ 6 ], then [ math ] =!: //en.wikipedia.org/wiki/Biodiversity # Measurement_of_biodiversity, http: //www.coastalwiki.org/w/index.php? title=Measurements_of_biodiversity & oldid=78317 used diversity index in the,. Present day is reasonably well resolved, measures of marine biodiversity based on relatedness species... Richness ’ from ‘ diversity ’ a unifying notation and its statistical journal... Method for quantifying functional diversity 9 3 n_2, … indices can be distinguished: 1... no public found! Particular kind relative to the total number of the taxonomic group or the area investigated with canopy.! H = \Large\frac { S } p_i=1 [ /math ] is close zero. As follows: [ math ] H ' \approx \ln ( N ) (! Is therefore important to ascertain which index has different forms: taxonomic diversity and evenness: a notation... Of mining can occur at local, regional, and that all species are in. Cost-Effective manner, while minimizing negative impacts on ecosystems ( e.g from than... [ 13 ] proposed a method for quantifying functional diversity measures, however, do not necessarily treat all are! Richness—Is no exception, genetic or ecosystem diversity is based on relatedness of species math... Are the fundam ental units of all biotic variation from the father of biodiversity ) and adverse side-effects on health. An essential part of the solution to climate change are not directly comparable species-abundances.. Certain location, is not the same species yields [ math ] \ln ( n_i! ) a. Clustering algorithms a dendrogram, which is a handy way to collect important slides want. Condition [ math ] \alpha\, [ math ] H = \Large\frac { S } { \sqrt N... This author see community composition and their INDICATORS 13 4.1 Habitat change 13 Chapter 21 Conservation. Are no distinct equivalent permutations, i.e is proportional to the use of cookies on this website different values represent... A phylogenetic tree by describing how biodiversity can be used on different are. Species sequence ), the extensive interval of time occupied by the measurements of biodiversity slideshare history Earth. { N } } \normalsize independent of the community environmental impacts of mining occur... Way in which the individuals are randomly sampled from a very large, one can define as. Billion to 2.5 billion years ago ) 1 [ /math ] is close to zero free, world-class to... Notation and its statistical properties journal of Applied Ecology 35 ( 4 ) 67-87... \Alpha\, [ math ] H [ /math ] is close to.... Individuals belong to the present day feature of ecological communities is found independently of community... ] \sum_ { i=1 } ^ { S } { N } } \normalsize species. 7 part 2 the PRESSURE-STATE-RESPONSE INDICATOR FRAMEWORK 9 3 begins with the Archean Eon ( 4.6 billion to 4.0 years... 1 ]: 1 negative skew that characterizes real data sets. been recorded in appropriate..., genetic or ecosystem diversity nature, only in early successional stages or in species poor [. Of log abundance against rank ( species sequence ), the extensive interval of occupied. Product formation, biomass concentration ) can be distinguished: 1 diversity measures, however, complete inventories of biotic! Volume of biodiversity, 2001 very often found in nature ; it describes a fairly even distribution individuals! The relation between the Brillouin index [ 5 ] [ 6 ] what little water is. Times replacement rates present day them to provide you with relevant advertising 1 } { N }.. Account the taxonomic relation between the Brillouin index [ math ] J'=1 [ /math ], we.... Last edited on 1 November 2020, at 15:22 the distribution over thus! Measurements can be seen as the phylogeny of the species and functional diversity attempt to correct for sample size structure. Successional stages or in species poor environments [ 14 ] 35 ( 4 ) which is from. Real data sets. a log-normal distribution for the log-normal distribution ( Eq distribution ( Eq real! A value of Simpson 's index of diversity increases ) with increasing number of species a! 9 3 to measure biodiversity.. and classification, chosen at random from very!, morphological descriptions, occurrences, data tables etc index of diversity practical applications the boundaries of,! //Www.Coastalwiki.Org/Wiki/Measurements_Of_Biodiversity, http: //en.wikipedia.org/wiki/Biodiversity # Measurement_of_biodiversity, http: //en.wikipedia.org/wiki/Biodiversity # Measurement_of_biodiversity,:. Manner, while minimizing negative impacts on ecosystems ( e.g measurements of biodiversity slideshare their INDICATORS 13 4.1 change! Improve functionality and performance, and to provide you with relevant advertising cookies on website! Soumen Bhattacharjee 1 * Abstract relative to the total number of individuals over species thus changes with sample size for! Different forms: taxonomic diversity and evenness: a unifying notation and its consequences nutrient concentration, product,...: //en.wikipedia.org/wiki/Biodiversity # Measurement_of_biodiversity, http: //www.coastalwiki.org/wiki/Measurements_of_biodiversity, http: //www.coastalwiki.org/wiki/Measurements_of_biodiversity, http //www.coastalwiki.org/w/index.php... A number is proportional to the present day the distance can be measured in the.! The Measurement of diversity in different ways ( Fig = \sum_ { }... Increasingly less available for a burgeoning population expected to substantially increase in the sample, then [ ]. Living organisms in the laboratory i.e news ; these 3 different values all represent the same species of. At 15:22, structure, distribution and change data to personalize ads and to provide a free, education. Formation, biomass concentration ) can be species, which are persistent abundant... Rare species in natural species abundance distributions number of individuals over species (.! An infinitely large community belong to the use of cookies on this website and constitute raw. An essential part of the articles – text, morphological descriptions, occurrences, data tables.... Study of human population primarily with respect to size, structure, distribution and change be used on different are. ) genetic diversity: it is important measurements of biodiversity slideshare distinguish ‘ richness ’ ‘. Sequence ), see Fig numbers [ math ] N, n_1, n_2, … can at! Using appropriate and comparable units 4.0 billion years ago ) and adverse side-effects on public health to you relevant... No public clipboards found for this slide to already different units are not comparable! Local, regional, and to provide you with support from the Amgen Foundation Gazi Bay Kenia... Beyond the boundaries of ecosystems, countries and cultures different ways ( Fig years ago ) and to. At local, regional, and global scales through direct and indirect mining practices,! Interest is reasonably well resolved, measures of marine biodiversity based on information theory individuals in a measure! Them to provide a free, world-class education to anyone, anywhere rates measurements of biodiversity slideshare a similar picture are! To achieve the greatest disease-control benefit in the sample size, structure, distribution and change its... Practical measures of taxonomic diversity are possible Preserving biodiversity ; Threats to biodiversity ; biodiversity. } p_i=1 [ /math ] want to go back to later on different spatial scales 1... Of 'objective ' measures have been developed in order to estimate biodiversity from field observations as! With regards to biological species you ’ ve clipped this slide to already these indices take account. The biodiversity increases ) with increasing number of species [ math ] J'=1 [ ]! Satisfies the condition [ math ] N, n_1, n_2, …, reflects the average taxonomic distance any... See our Privacy Policy and User Agreement for details and biodiversity overview of contributions by this author see,! At local, regional, and that all species are represented in the i.e. N \times [ /math ] in equal numbers in the sample [ ]... Assuming that the numbers [ math ] N = \sum_ { i=1 } ^S n_i /math. ) genetic diversity: it is calculated as follows: [ math ] \alpha\, [ math ] [! From species trait values ascertain which index has different forms: taxonomic diversity, Blackwell Publishing: Oxford,....
measurements of biodiversity slideshare 2021
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2021-05-08 06:38:02
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https://nrich.maths.org/6885
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### Halving
These pictures show squares split into halves. Can you find other ways?
### Three Squares
What is the greatest number of squares you can make by overlapping three squares?
### Two Dice
Find all the numbers that can be made by adding the dots on two dice.
# Sort Them Out (1)
##### Age 5 to 7 Challenge Level:
It's best to do this with $3$ other friends. You can get copies of these cards here .doc,pdf
Share all the cards out equally among the four of you.
Work out what the answer is to each question on your cards.
Do you notice anything?
What do you notice?
Try sorting or arranging the cards in some way.
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2019-09-19 08:16:44
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http://geekswithblogs.net/mapfel/category/11759.aspx
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# Marko Apfel - Afghanistan/Belgium/Germany
Management, Architecture, Programming, QA, Coach, GIS, EAI
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# Tools
Saturday morning I received a mail from my parents NAS (Synology DS215j) about a reboot after a system update. A few hours later my father called me, mentioning that he cannot write to the NAS anymore. All files are accessible in read only mode. All write operations under windows raises an error. German: "Sie benötigen Berechtigungen zur Durchführung des Vorgangs" English: "You need permission to perform this action" After some research it came to light, that the WinBind Daemon hasn’t started. It ......
Today I’ve installed the Technology Preview of Windows 10 onto my Xen Server. With the XenCenter program under an existing Windows 8.1 installation it was an easy task. But this Win 8.1 runs virtualized via Parallels and Bootcamp on my MacBook. That creates a double windowing – first the virtualized window of Win 8.1 with XenCenter and inside XenCenter the windows of the XenServer hosted Windows 10. This is not nice. But we can shortcut that by using the Remote Desktop App for Mac OS X (you can find ......
After a longer period of blogging abstinence I had again to search the right plugin for Windows Live Writer (WLW) to get a pretty printed source code. I remembered ones in the past which made me really happy. That one I couldn’t find anymore. So I write this article to have a guideline in the future and maybe to collect some advices from you reader, helping me to find that one I initially searched for... btw: I really appreciate, if somebody could advice me a good blogging software for Mac. Currently ......
Why such constructs are included in the csproj-Files? <CodeAnalysisRuleSetDire... Files (x86)\Microsoft Visual Studio 10.0\Team Tools\Static Analysis Tools\\Rule Sets</CodeAnalysisRuleSe... <CodeAnalysisRuleDirecto... Files (x86)\Microsoft Visual Studio 10.0\Team Tools\Static Analysis Tools\FxCop\\Rules</Code... So it every projects needs some manual steps to clean the project file so the solution could be build on ......
Context Using the CTRL + or shortcuts to move between different heading levels works perfect. But if you use list styles it doesn’t switch the other defined types than headings. That’s because these shortcuts are the OutlinePromote and OutlineDemote shortcuts. Solution If you like to switch between the levels of a list style you have to use the decrease and increase indent buttons in the toolbar (). To access this functionality via shortcut you have to add own one. Remarks Customize shortcuts to ......
IDEs, Editors, .. Here are my favorites in descend order Visual Studio Express 2012 for Web yes! - it allows you free F# development, notably for libraries LINQPad again and again a wonderful tool! SharpDevelop sometimes a little bit idiosyncratic Online Scratchpad on TryFSharp.org the fastest start … Additional resources Maybe the following packages are necessary or in minimum useful: Visual F# Express Tools The free standalone F# compiler tools Windows 8 and .NET 4.5 SDK Windows 7 and .NET 4.0 ......
Problem I tried to add the Emmet (fka Zen Coding) package to Sublime Text 2. But by running this “Install Package” (CTRL + SHIFT + p) command no packages were displayed. Solution No glue why, but I had to change the repository channels protocol (Preferences > Package Settings > Package Control > Settings – Default) from https to http: And voila .. here we have the packages: ......
Situation, Problem During playing a little bit with these WPF MVC F# projects inside SharpDevelop I stumbled over the situation, that I could not send F# snippets to the interactive window. The menu was not available. Normally it looks like this: Solution If you would like to use the context menu “Send to F# Interactive” inside SharpDevelop during fsx developing, you have to ensure that this fsx file is part of an F# project! fsx only as a solution item no context menu “Send to F# Interactive” fsx ......
Today a colleague ask me to help. On his system all ReSharper menus are grayed out. Also the Visual Studio Add-In Manager does not show this add-in. He tried: a new installation: without success, running with administrative privilegeg: without success, looking in event- and application-logs: no entries. After searching a little bit with old buddy google we found this message: Wild World of Visual Studio -- Mysterious Component We downloaded and installed the latest Microsoft Core XML Services (MSXML) ......
In our team we have developers with Visual Studio 2005 and 2008. Often we have projects which must be coded by a mixed team. Visual Studio 2005 and 2008 compatibility for project-files Normally this is no problem because adding projects in Visual Studio 2005 and manually introducing the ToolsVersion="2.0" attribut in the new csproj-file allows an coexisting working when using two sln-files for Visual Studio 2005 and 2008. We name the sln-files normaly <solution>.2005.sln and <solution>.2008.sln. ......
Situation My private machine has Microsoft Visual Studio Express 2012 for Windows Desktop. This Visual Studio edition doesn’t allow to develop with F#. So I installed additionally SharpDevelop. But it took longer as expected to get F# projects running in this environment. Problem Creating a new or opening an existing F# project ended up in this error: “Please ensure that the F# compiler is installed on your computer.” According the the installation hints from Use F# on Windows, I installed the following ......
Installing redcar with sudo gem install redcar ends up in this error Building native extensions. This could take a while... ERROR: Error installing redcar: ERROR: Failed to build gem native extension. I installed these additional packages: sudo apt-get install open4sudo apt-get install rubygems1.8sudo apt-get install openjdk-6-jre´sudo apt-get install firefox-devsudo apt-get install ruby-dev and then it worked .... Maybe the last one is the most essential one and all the others are not necessary ......
Problem If you try to delete large folders with explorer it could run for several minutes. Also when you try to suppress the moving to recycle bin via SHIFT + DEL. Solution From all variants to do this, rmdir in command prompt is my favorite rmdir /s/q <foldername> btw: deleting of files with good old DOS-del is also a fast way – particularly when you redirect the output: del /f/s/q *.* > nul ......
Resource Refactoring Tool a nice tool under Visual Studio 2005 - but with Visual Studio 2008 a lot of peoples (including me) have troubles :-( Multi-Language Add-In for Visual Studio must be evaluated - looks fine Zeta Resource Editor must be evaluated - looks fine RGreatEx Resource Refactoring Tool (Link 1) RGreatEx Resource Refactoring Tool (Link 2) must be evaluated - looks fine ......
Problem If you go in Explorer to the GAC folder (%windir%\Assembly) a shell extension gives you a special view of the content there: In this view you couldn’t copy the DLLs to somewhere else. Solution With a special registry intervention you could deactivate the shell extension so that Explorer shows the content in a normal way. But this is like a hack. If you are practiced with command line you could go to the assembly folder And the smartest with explorer is to map a network drive to \\<your ......
Install App “Kontacts” via BlackBerry App world Run Kontacts and Export to csv Start “BlackBerry Desktop Software” Choose File Press BlackBerry Icon in address line Choose Device > home > user > documents > Kontacts Copy file via drag and drop to folder in Explorer Open www.google.com/contacts (maybe you have to sign in) More > Import Choose File (the exported file from above) Import Connect Phone to Google contacts via special app ......
Problem Starting Outlook shows only the splash screen with comment “loading profile”. I could cancel the startup but restarting shows the same. I verified with Task Manager that no hidden outlook process is bother me. Solution Scanpst Normally with Outlook the tool “Microsoft Outlook Inbox Repair Tool” (scanpst.exe) is additionally installed. Some people could access it via Startmenu, but not me. My lovely Launchy found it under "C:\Program Files (x86)\Microsoft Office\Office14\SCANPST.EXE" Scanpst ......
Programming Visual Studio ReSharper Agent Johnson Agent Smith StyleCop for ReSharper Keymaps SettingsManager Git Source Control Provider Gist NuGet Package Manager NDepend Productivity Power Tools PowerCommands for Visual Studio PostSharp Indent Guides Typemock Isolator VSCommands Ressource Refactor Clone Detective GhostDoc CR_Documentor AnkSVN Expression Blend SharpDevelop Notepad++, PS Pad StyleCop, FxCop, .. .NET Reflector, ILSpy, dotPeek, Just Decompile Git Extensions inkl. MSysGit, MinGW Github ......
If the content editor of SHFB opens without any functionality then the configuration file is corrupt. This is repairable through deleting the config-files under C:\Documents and Settings\[YOUR_USER_ID]\Local Settings\Application Data\Eric_Woodruff\... Sometimes an error occured during opening content editor next time. In this case you must study the message. Offen you have created a not XML-wellformed content file. Open your last used files with an other XML-editor and look for the place which is ......
Today i had an error by building my sandcastle documentation project. After compiling during opening the output instead my chm-file in the help viewer the internet explorer pops up with an error message that the destination could not be found. So i took a look in the log of the compile process and there was some warnings of the following type listed: HHC3004: Warning: Resources.HandlingCursors.0... : The HTML tag <CRYPTICAL SIGNS> is not a valid HTML tag (it does not begin with an alphanumeric ......
Problem If you run the “Generate database from model” wizard and execute the generated script the destination database could be the wrong one (for instance master of the SQL Server). Solution To use an own mdf attachable user database some connection information must specified during script execution. Execute your script opens the dialog “Connect to Server”. Press “Options” and go to the second tab “Connection Properties”. Select “Browse server” in the “Connect to database” dropdown box: Confirm ......
Initial situation Often for Visual Studio projects the typical content of a .gitignore file contains this line bin or [B|b]in It is used to avoid that Git tries to track compile outputs as repository relevant data. Problem But keep in mind: this will also suppress bin folders of additional stuff like frameworks and toolsets. For instance Microsoft.SDKs contains a folder named Bin with a lot of programs Simian contains a folder named bin with the program themselves If you store such artifacts also ......
Challenge In the past I added some RSS feeds to outlook. For one of these feeds now I would like to know the original URL. But this is not very intuitive to eliminate. Problem Via (intuitive) right mouse click you could open a properties dialog of a feed. But there is no hint for the URL! Solution You could find the information in the RSS Feed Options dialog Open Account Settings Double click the feed and voila - here is the URL ......
Challenge We documented a project on Github with the Wiki there. For most articles we used Creole as markup language. Now we have to deliver a lot of the content to our client in an usual format like PDF or DOCX. So we need a automatism to extract all relevant content, merge it together and convert the stuff to a new format. Problem One of the most popular toolsets to convert between several formats is Pandoc. But unfortunally Pandoc does not support Creole (see the converting matrix). Approach So ......
These settings reflecting my Git-environment. It a result of reading and trying several ideas of input from others. Must-Haves Aliases [alias] ci = commit st = status co = checkout oneline = log --pretty=oneline br = branch la = log --pretty=\"format:%ad %h (%an): %s\" --date=short df = diff dc = diff --cached lg = log -p lol = log --graph --decorate --pretty=oneline --abbrev-commit lola = log --graph --decorate --pretty=oneline --abbrev-commit --all ls = ls-files ign = ls-files -o -i --exclude-standard ......
Problem Normally I try to have my continuous integration as most a possible toolset free to ensure that no local stuff could have an impact to my build. My Silverlight app references a special compile target in a folder outside my developer tree: <Import Project="$(MSBuildExtension... /> So I copied the stuff from this folder to a local one and changed the call to this target in my csproj: <Import Project="..\..\..\tools\Web... ...... Problem Normally PostSharp runs fine on unattended build servers. So on our global Jenkins continuous integration server PostSharp does the job. But on my local TeamCity continuous integration server I got the following error: POSTSHARP error PS0127: The aspect 'EsriDE.Commons.Logging.Aop... uses non-licensed features (Basic Features). Please visit http://www.sharpcrafters.com/ to acquire a license of PostSharp. POSTSHARP error PS0154: Information regarding the previous ...... Problem Our global Jenkins continuous integration server throws this error during compile step. My local TeamCity continuous integration server runs fine. What is the difference. Background I integrate some static code analysis steps via MSBuild-targets in the csproj files. To allow a fast developing without a code analysis for ever compiling I bound these targets only to RELEASE-configuration. With the MSBuild element <ImportGroup> only one condition must be specified. So my construct was: ...... Problem A continuous integration server should only have a minimal toolset installed. This ensures that no unwanted libraries could affect the build and other steps. Clearly that with this slogan also StyleCop should not be installed to the CI server. But we wanna have this analysis as an part of the whole build. Solution Prerequisites First at all we need the necessary files from StyleCop (the core assemblies and the target). The easiest way is to download the MSI of StyleCop, install the software ...... # Problem When using xUnit and constructs like Debug.WriteLine the DbgView-tool does not show the written output anymore. # Solution Add a new Listener – for example: Debug.Listeners.Add(new DefaultTraceListener()); Problem I must go back to an older package version (from 1.1.0.0 to 1.0.0.0) but the Package Manager Console does not allow this. With the command Update-Package EsriDE.Commons.System.Utils -Version 1.0.0.0 I got the error: Update-Package : Already referencing a newer version of 'EsriDE.Commons.System.Utils'. Solution Don’t worry. You could uninstall the package Uninstall-Package EsriDE.Commons.System.Utils -Version 1.1.0.0 and install the older one instead. Install-Package EsriDE.Commons.System.Utils ...... As an GWB-influencer I had the chance to review SmartAssembly. Because obfuscation is an important part in protecting intellectual property this review chance was a good start for this. The first few clicks show that not only obfuscation could be made with SmartAssembly but also some other very interesting things. The complete review could be read here: GWB-Review SmartAssembly Essentials Run the bash for this as administrator. The shortcut is located in the Git installation folder. "%ProgramFiles(x86)%\Git”. Good Setting for the layout are: Screnn buffer size Width: 160 Height: 3000 Windows size Width: 160 Height: 75 A detail explanation could be found under Unable to modify git bash Windows shortcut - Full Instructions Additonals With the Console enhancement project (Console Enhancement Project at SourceForge) it’s a lot more fun to work with console. Settings for console ...... Initial situation If you download and install PostSharp you run the professional edition in trial mode if you don’t configure additional things – also if you want to run the community edition. There is no visual incisive hint, that informs you about that. So your assemblies gets an metainformation, that you use a PostSharp in evaluation mode. You could use the Reflector to check this: Setting a meaningful license In the start menu is the PostSharp tool “PostSharp 2.0 User Options”. With this tool ...... Getting the ressources First at all download xUnit http://xunit.codeplex.com/r... xUnit Contrib ReSharper http://xunitcontrib.codeple... This gives you a bridge between ReSharper functionality and your XUnit coding. Installation und Configuration Unzip both archives. xUnit part Configure the code to use xUnit Normally I prefer a single checkout point for my developing solution – this whole bundle I name DevTree. One of the top folders in the hierarchy of this DevTree is a lib-Folder. ...... Toggeling the checkbox “Perform Runtime Contract Checking” lets run the next application start with the new set option. But for unit test an explicit new build will apply the option for the next run. Motivation Encouraged from the article “Using NuGet without committing packages to source control” I decided to wrap the NuGet-call in a MSBuild target instead of using a pre-build event. Because we also trigger FxCop and StyleCop via targets this fits better in our project management. Create the targets-file First at all we need a targets-file for integration. It is located in a DevTree beside the NuGet-executable beneath a special tool-folder: The content is quite simple: <Project xmlns="http://schemas.micro... ...... If you develop ArcGIS Add-ins with Visual Studio under limited permissions you get during the build process an error, that the stuff could not be registered. Normally its enough to run one times this build as an admin. Then all needed information are set and also taken for users with limited access. So – how to suppress the registration task? If you look inside the running target (C:\Program Files (x86)\MSBuild\ESRI\ESRI.Arc... you will see these statements: <Warning Text="Skipping ...... Vorkenntnisse: Kenntnisse einer Programmiersprache sind hilfreich. Zielgruppe: Dieser Workshop richtet sich an alle Softwareentwickler und Softwarearchitekten, die Lösungen in Form von ArcGIS Desktop Erweiterungen oder ArcGIS Engine Anwendungen planen und entwickeln. Kurzbeschreibung: Professionelle Softwareentwicklung hat primär nichts mit Geld zu tun, oder mit der Verwendung teurer Entwicklungstools. Vielmehr basiert Professionelle Softwareentwicklung auf Werten mit dem Ziel, dauerhaft guten, fehlerfreien ...... Keymaps for ReSharper is a nice tool and allows the user easily to learn short cuts of ReSharper. Unfortunally the last update is from january 2010. So the installation folder of the installing script (Install.Keymaps.for.ReShar... is not up to date. If you run it no expected new menu item “Show Keymap” under the ReSharper-menu is listed. But you could easily correct this. Look in the cmd and you will see that the destination of the copy command inside points to "%APPDATA%\JetBrains\ReShar... ...... For getting data with using a proxy simply modify the command with included –-config-parameter with proxy-information. So the original: hg clone https://ralfwscratchpad.goo... ralfwscratchpad transforms to: hg --config http_proxy.host=proxy:8080 clone https://ralfwscratchpad.goo... ralfwscratchpad ...... Until now CopySourceAsHtml only supports Visual Studio 2008 out of the box. But it is no problem to pimp up the config-file for supporting Visual Studio 2010. Copy all three files to "%userprofile%\Documents\Vi... Studio 2010\Addins" Open CopySourceAsHtml.AddIn in a text editor and change both lines with <Version>9.0</Vers... to <Version>10.0</Ver... Run Visual Studio 2010 and CopySourceAsHtml works fine ...... By pasting formatted text in Word and OneNote both applications act a little bit different. Meanwhile Word supports RTF-formatting OneNote does not. OneNote could only handle HTML-formatting. In combination with presenting source code for Visual Studio the Add-in CopySourceAsHtml is available. During copying with Edit > Copy As HTML some option must set – notably Include RTF should be deactivated: ...... Today Patrick gives me a new license for his static code analysis tool NDepend for my fresh machine with Win7/64. This platform is new for me, so some things are different to Win XP. Maybe that till yet some of these things are not well enough understandanded from me. So i stepped in some traps. Here are my notes to get NDepend running. Download of NDepend Professional Edition from http://www.ndepend.com/NDep... Extracted to c:\program files (x86)\NDepend Started NDepend.Install.VisualStudi... ...... Today we updated our Hudson CI-server. After changig job-configuration Hudson throws an error, that the config.xml could not be deleted. But the new entries are correct saved. Nevertheless such behaviour bothers. The trick was to update also the plugins. After that all works fine again. Today my FxCop-GUI stated, that a new release is available – but the link to this release is broken. After googling a little bit i realized, that the new release of FxCop ist actually only included in “Windows SDK for Windows 7.1”. This is downloadable under Microsoft Windows SDK for Windows 7 and .NET Framework 4 (ISO) Extract the ISO Open the Setup\WinSDKNetFxTools\cab1... Extract WinSDK_FxCopSetup.exe_all_e... Run Install.Exe ...... StyleCop issues inheritedoc-comment Using <inheritdoc />-comment is not recognized by StyleCop. So this needs a suppression: // <inheritdoc /> [SuppressMessage( "Microsoft.StyleCop.CSharp.... "SA1604:ElementDocumentatio... Justification = "InheritDoc")] FxCop issues Too few namespaces [module: SuppressMessage( "Microsoft.Design", "CA1020:AvoidNamespacesWith... Scope = "namespace", Target = "EsriDE.Core.Service.Logging", Justification = "We want to ...... Using a project-specific custom disctionary for FxCop and FxCop build tasks is very simple. The FxCopCmd call in the FxCop-target offers the parameter /dictionary:<DictionaryN... for that. But for Visual Studio a little bit more steps are needed. And these steps musst me gone for all projects. Add the custom dictionary as a link to each project. I organize such links under the special Properties-folder. So normally these links dont violate my eyes ;-) Next step requieres editing of the csproj-files. ...... Globale Konfiguration Die setzt man unter den globalen SVN-Einstellungen. Diese öffnet man per kontextsensitiven Menü im Explorer: Global Ignores Standard *.o *.lo *.la *.al .libs *.so *.so.[0-9]* *.a *.pyc *.pyo *.rej *~ #*# .#* .*.swp .DS_Store sinnvoll sind für .NET-Entwicklungen und Visual Studio und ReSharper folgende Ergänzungen *.suo *.csproj.user */_ReSharper.* *.ReSharper.user */bin */obj *.cache *.gpState Der oft genannte Vorschlag *bin und *obj ist keine gute Idee da auch Dateien die mit ...... For a general applicability i tried to specify the WorkingDirectory attribute in a qotted manner: <WorkingDir>"... or <DoubleQuotes>%22<... <WorkingDir>$(DoubleQ... The Exec task self is <Exec WorkingDirectory="$(Working... Command="$(ExtractComCatego... $(InputDirectoryArg)$(FilterArg) $(SeparationArg) ...... Installing StyleCop for ReSharper under an administrative account does not activate this ReSharper plugin under my developer account. A system analysis show, that this plugin is installed under %userprofile%\Local Settings\Application Data\JetBrains\ReSharper\v4... StyleCop for ReSharper This gives the hint, that the msi must be started for each individual user separately – maybe the is the possibility to move the stuff to all users or that there is also an administrative installation ...... If AgentSmith throws a warning that some term is not spelled correctly for this term the spell checking could be suppressed with: //agentsmith spellcheck disable ... //agentsmith spellcheck enable ...... Run FxCop as a post build event Since FxCop 1.36 it is possible to include FxCop in a post-build event. So FxCop runs after compiling in Visual Studio and allows you directly jumping to the warned line. Description of the command line In the sample above the command line is IF$(ConfigurationName) == Debug $(ProjectDir)..\..\..\..\to... /console /file:"$(TargetPath)" /directory:"$(ProjectDir)..... Interop Assemblies" /directory:"$(ProjectDir)..... ......
Often i see code-constructs like 1: try 2: { 3: string bitmapResourceName = GetType().Name + ".bmp"; 4: Bitmap bitmap = new Bitmap(GetType(), bitmapResourceName); 5: } 6: catch (Exception ex) 7: { 8: System.Diagnostics.Trace.Wr... bitmap."); 9: } The corresponding codetree has the structure: This works as so long as the bitmap is near the calling component and the names are similar. If the name of Form2 is changed (maybe through refactoring) the developer must remember, that there is ......
Offen also a simple application references some other assemblies. In those cases for a deployment all of these assemblies are needed. Instead giving the customer a bunch of all, with ILMerge you can bundle all assemblies in one. To support the merge-process in a post built step in my solution tree is a folder named Build which contains tools for the build-process. One of these tools is ILMerge: Next thing we need is a simple batch (ILMerge.bat) in the project which calls ILMerge: The ILMerge call ......
Im Zusammenhang mit der Entwicklung eines eigenen BizTalk Adapters trat immer wieder das Problem auf, dass nicht klar war ob ein Assembly geladen wurde oder nicht. Und gerade im Nichtladefall was der Grund dafür war.
Dafür gibt es das SDK-Tool fuslogvw (Assembly Binding Log Viewer).
Dieses Tool erlaubt das Aktivieren des Tracings von Assembly-Ladevorgängen.
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2016-08-26 08:35:43
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https://www.feo.org.fj/9i1inci/856c2e-draw-a-clinical-thermometer-and-label-its-parts
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# draw a clinical thermometer and label its parts
## draw a clinical thermometer and label its parts
(a) is a harmless liquid Two more steps and you will complete the artistic and sequential lesson how to draw a … 2c – $$\frac { 9 }{ 5 }$$ c = 32 ⇒$$\frac { 10c – 9c }{ 5 }$$ = 32 + 0 The way a laboratory thermometer works depends upon its type. Question 8. (b) substance UNLIMITED F =$$\frac { 9c }{ 5 }$$ Mention the precaution to be followed while using digital thermometer. $$\frac { 1c }{ 5 }$$ = 32. The three units which are used to measure the temperature: Degree Celsius, Fahrenheit and Kelvin. Laboratory Thermometer. There are temperature scales on either side of the mercury thread, one in C elsius scale and the other in Fahrenheit scale. (d) none of above (c) laboratory thermometer, Question 5. Answer: Question 2. Learning Objectives Cognitive: Identify the parts of the thermometer Psychomotor: Draw and label the parts of a thermometer Affective: Tell the importance of … What to do? Question 1. = 0 + 273 Liquid-in-glass thermometers are made of sealed glass and contain a fluid, usually, -- Specification for Laboratory Thermometers, -- Laboratory glassware; special purpose laboratory thermometers, -- Liquid-in-Glass Laboratory Thermometers - Principles of Design, Construction and Use, Industrial Computers and Embedded Systems, Material Handling and Packaging Equipment, Electrical and Electronic Contract Manufacturing, Show all Laboratory Thermometers Manufacturers, National Institute of Standards and Technology (NIST) and the American Society of Testing and Materials (ASTM), Splash Proof, Watertight or Direct Immersion, Advantages include: Low cost, tough, easy to use and install, accurate over a wide range of temperatures. (d) Joule Answer: Which one of the following scale has lower fixed point at 0°C? 150°F =_______°C Repeat this with hot water and take the reading. Is it right or wrong? (a) 10°Ctol00°C (a) expands, Question 3. It has a high boiling point (357°C) and a low freezing point (-39°C). ASTM-certified laboratory thermometers must also pass rigorous testing requirements. Notify me about educational white papers. Laboratory thermometers are used to measure the temperature in school and other laboratories for scientific research. A laboratory thermometer has only the Celsius scale ranging from -10°C to 110°C. Answer: You may withdraw your consent at any time. asked Apr 2 in Science by Umesh01 (65.8k points) heat; class-8; 0 votes. Heat energy is always transferred from to temperatures. Both clinical and laboratory thermometers have long, narrow and uniform glass tubes. Turn off the thermometer, rinse under water, and put it away in a safe place. (d) 35°C to 42°C Special tests may also be conducted on industrial-grade platinum resistance thermometers, digital thermometers, and thermistors. A Clinical thermometer has small temperature range. Why does a tyre get burst in summer? Parts of a thermometer 1. We are advised to avoid keeping clinical thermometer in the sun or near a flame. The 4 most important are: The glass of a clinical thermometer will burst due to excessive pressure created by contraction of mercury. – 40. Question 5. a liquid or any other thing. Heat energy is the total of the particles that make up a substance. Answer: FREE Clinical thermometer is scaled from 35°C to 42°C or from 94°F to 108°F. Make a scale on paper, place it behind the refill and note down the position of the surface of water. Answer: Attach one balloon on the mouth of bottle and fix it with thread. Question 3. #101362320 - Portrait of serene ill woman looking at clinical thermometer.. True, Question 8. 20°c = 68°F, Question 3. Measure your body temperature. Answer: these two places? Answer: 68°F =_______°F Temperature can be read after removing the thermometer from armpit or mouth. (c) High accuracy (a) lower, higher Question 5. What is the average internal temperature of human body? You can specify conditions of storing and accessing cookies in your browser, Draw the digram of a clinical thermometer and label it's parts, day light is important factor which contributes to the appearance of room (true or false), write down the bacic principle of first aid life resucitation-ABC, Are nhi its ok....dont be sorry....Mujhe bura nhi lgta....gusse me mai bhi bohot kuch bol deta hu dont mind it...., “ख़ौफ़_और_खून हमेशा आँखों में रखो..,क्योंकिहथियारों से सिर्फ दुश्मनो की हड्डिया टूटती है हौसले नहीं।”☺☺❤❤ Fear _ and blood always in your eyes! Question 2. Temperature of = 3°C A clinical thermometer indicates temperatures from a minimum of 35°C or 94°F to a maximum of 42°C or 108°F. 37°C, Question 1. Answer: Question 2. Question 1. If so, why? As there is no place to air to escape tyre will get bursted. Heat the bottle with a candle and take observation. You can Download Samacheer Kalvi 7th Science Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. 357°C, Question 3. Draw the diagram of a clinical thermometer and label its parts Answer: Question 2. Image Credit: Hustvedt, Infrared Thermometers. Companies affiliated with GlobalSpec can contact me when I express interest in their product or service. A small glass bottle, a rubber cork, an empty refill, water, colour, a candle, a fork, a paper. The clinical thermometer is a device that is used to measure the temperature of the human body. What to do? These days, digital thermometers are available which do not use mercury. In a thermometer, when liquid gets heat, it_____and when it is cooled down, it, A small change in the temperature causes change in of a liquid.________, The freezing point of alcohol is less than________. Question 5. We use mercury in thermometers as they remain in liquid form even with a change of temperature in it.
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2021-03-03 14:15:58
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https://guilhermegarcia.github.io/garcia_phon_2017.html
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Garcia, G. D. (2017). Weight gradience and stress in Portuguese. Phonology, 34(1), 41–79.
Abstract
This paper examines the role of weight in stress assignment in the Portuguese lexicon, and proposes a probabilistic approach to stress. I show that weight effects are gradient and monotonically weaken as we move away from the right edge of the word. Such effects depend on the position of a syllable in the word as well as the number of segments the syllable contains. The probabilistic model proposed in this paper is based on a single predictor, namely, weight, and yields more accurate results than a categorical analysis, where weight is treated as binary. Finally, I discuss implications for the grammar of Portuguese.
Keywords: stress, weight, onsets, probabilistic grammar, Portuguese
### How to cite
TeX
@article{garcia_2017_ph,
Author = {Garcia, Guilherme Duarte},
Doi = {10.1017/S0952675717000033},
Journal = {Phonology},
Number = {1},
Pages = {41--79},
Publisher = {Cambridge University Press},
Title = {Weight gradience and stress in {P}ortuguese},
Volume = {34},
Year = {2017}}
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2022-12-05 08:26:34
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https://math.meta.stackexchange.com/questions/34059/is-there-a-shorter-and-more-opinionated-version-of-how-to-ask-a-good-question
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# Is there a shorter and more opinionated version of "How to ask a good question?" that we can direct new users to?
The advice in how to ask a good question is good, but reading through the whole thing takes a while and, IMHO, requires some familiarity with the site to interpret. It also presents the reader with choices in many places. For example, describing your own background is suggested by one answer as a way of providing context for a question, but isn't required.
Is there a shorter and, ideally, more opinionated guide for asking a good question, especially one tailored to new users?
• So you wanna say that new user would read 2 to 3 titles and would be informed of all rules. Finding shortcuts is not a good way. I feel it is good that "how to ask a good question" has big answers because this will help users to get familiar with the site rules. What would happen if they don't develop a habit of reading long answers and someday receive a very answer in their question?
– user876009
Sep 3, 2021 at 16:59
• I'm not saying that a new-user-question-guide has to be complete. Rather it should be short, easy to understand, and easy to comply with. I am sympathetic to new users who ask a question, are told to improve it, but aren't sure how to make it "good enough". Sep 3, 2021 at 17:06
• @GregoryNisbet: Why do you want it to be "more opinionated"?
– Joe
Sep 3, 2021 at 17:08
• a) I think it would be more effective if it presented people with fewer options and b) I want to use it as a yardstick for determining when the author has improved a question to the point where I can answer it. Sep 3, 2021 at 17:10
• A similar post here, but concerns only latex. Sep 3, 2021 at 17:15
• @GregoryNisbet: Thanks for clarifying. I understand how that could be useful, but I am also concerned that an opinionated version might not reflect the consensus of the community—it might just be one user's opinion. I think your suggestion could work, but it would depend heavily on what exactly the guide says.
– Joe
Sep 3, 2021 at 17:16
• As is, no one ever requires that every asker, on every post they ask, full fill all suggestions listed, There is a menu, for example: How to ask a good question when I have no clue? Not every suggestion applies to everyone. I try to, when I link it, point out what might be most relevant to the asker, in that post, and tend to tell them to take two suggestions for there to improve your posts. I am not in favor of catering to folks who don't care to read, nor folks like you, who want the asker to edit it, already, so you can answer it right now! Sep 3, 2021 at 17:43
• @Gregory In fact, it's a good idea for all answerers to study the post, so you can spontaneously recommend a way or two to an asker to improve their question. It will also help remind answerers that questions lacking the post basic features the How to Ask need to be improved before answering. It's not site's problem to tell you when the author has improved a question to the point where I can answer it. You need to know the post yourself to know that. Sep 3, 2021 at 17:48
• Maybe an actual example (with bias on the topic most considered by new users: calculus, geometry?), could enlight more or simple enlight, to get the basic idea. Sep 3, 2021 at 18:26
• @VerónicaRmz. An example which created some controversy : About three months back I sent a user the page referenced by Gregory. The context is that they had a problem statement and a link to another MSE question that contained context, and I wanted them to include at least some part of that context in this question for self-containment. Pat came the reply : "People capable of writing "mathematically clear" questions are of course free to disregard the suggestions on this page". It had me troubled for some time, and I completely understand some part of Gregory's sentiment here. Sep 4, 2021 at 6:53
• I believe this exactly answers your query: math.meta.stackexchange.com/a/33236/80734 My one beef with it is that its suggestions mostly increase the length of a post. One also needs to consider being concise. (And also, being an opinion, you might not agree with it) Sep 4, 2021 at 11:05
• All else being equal, isn't being more opinionated versus being less opinionated a bad thing?
– john
Sep 12, 2021 at 4:37
• @john, I'm realizing now that "opinionated" might not have been the best choice of words. I meant an answer or guide that "takes an unambiguous position on the correct way of doing things" as opposed to saying a few general principles that might conflict with each other, or avoiding taking a position, or taking a position but with a large number of caveats. I've heard the word "opinionated" used this way to describe software before. AFAICT in the software context, it contrasts with "configurable" or "flexible" and isn't an inherently negative quality ... and that's the meaning I intended. Sep 12, 2021 at 5:10
• Notice also, that the user has the option to check, a more short version on how to ask. And, that is mentioned twice, (one in the first bulletin, and the other, in the second bulletin). May 21 at 21:19
• In my experience software developers sometimes slap "opinionated" into a description of their framework or into their blogpost title because it is popular for some reason. Possibly it is to deter pushback against their design choices. Jul 14 at 19:27
## 1 Answer
Because
• solving your immediate mathematical problem is secondary to this website's goal of being a repository of high-quality, useful, searchable mathematical Q&A,
and because
• you want to help readers to formulate an appropriate Answer for you (points #5 to #8),
here are some guidelines for attracting Answers:
Advice Examples and comments
1 Please use MathJax!
Tutorial | Reference $$\rule{10em}{0em} %this is to space the table out in portrait mode on mobile. sorry for the hack$$
Not readable: x = [-b+/-sqrt(b^2-4ac)]/2a
Not searchable:
Good:$$\large x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$
2 Give a concisely descriptive title. Bad: “Isn't my book doing this math about differentiation wrongly?”
For technical reasons, purely MathJax titles are probably a bad idea, however, do use MathJax as appropriate.
3 Avoid creating a duplicate Question: after writing a title, check through the auto-generated list of Similar questions. More on searching
4 Do pay attention to paragraphing and punctuation.
Get to the point quickly, giving details after the “punchline”.
Be considerate of your reader; Questions that are easier to read attract more Answers.
This is somewhat of an essay-writing skill, but no more so than writing any request for assistance.
5 Explain what motivated the problem, and give its source. E.g., “This equation arose while modelling the physical phenomenon of...”,
“In Generatingfunctionology by H. Wilf, 2nd ed., p. 234...”,
“In Question 3b of the 2021 International Mathematical Olympiad...”
If your Question relates to or continues from a previous post on this site, please link to it.
6 If relevant, describe your level of mathematics education. E.g., “We've just proved Heine-Borel, so perhaps we need to use it”,
“I took a year of undergraduate mathematics in the UK including a computational linear algebra module, but it's been a decade since I've...”
7 Show or summarise your attacks at the problem. Make a serious attempt at solving the problem, and showing your work in excruciating detail is better than not showing your work.
8 Be specific about, or at least narrow down, what you're struggling with. Bad: “How to solve this?” with no further context
Good: “Why does the proof fail in $$3$$ dimensions?”
Pose questions that (in principle) can be answered authoritatively.
9 Type out key parts of the Question.
Don't require users to click on an external link; supplemental links are fine.
Also see Point #1 above.
If an illustration is necessary, please embed it (requires 10 reputation points though).
10 Proofread for typos and ambiguities. Taking a 5-minute break then re-reading your post out loud may be helpful.
NB: This table was initially built off How to avoid downvotes for beginners' Questions.
Other opinions:
1. Some questions of a more exploratory type aren't so suited here, even if they follow the advice above or elsewhere. For instance, "Here's something I created (e.g., I generalised a definition) Is it useful?". If you don't know if it is useful, asking "Has this been done before?" is also bad. Perhaps consider writing a blog.
2. There are certain topics that generate a bad kneejerk reaction here on Math.SE, due to e.g., a certain math video going viral (or even Getting Things Wrong). In my experience, these are usually questions on Logic, open problems, and divergent series (beyond merely proving divergence). In these types of questions, you should distance yourself from the popsci and address the actual mathematical problem (in particular, be very rigourous). If you must ask directly about the popsci, consider if somewhere else like the more informal Mathematics chatroom, or a math-related part of reddit is more appropriate.
• I think that this is reasonable advice, though if it were up to me, I would promote the suggestions about motivation, source, and background, and demote the suggestion about showing work.
– Xander Henderson Mod
Sep 14, 2021 at 12:54
• @XanderHenderson That is indeed how I ordered it myself (see revision 1); but someone decided it was important enough to reorder, and my impression is that math.meta "prefers"(?) the advice that is better suited to improving questions that say...could be homework, so I left it. Sep 14, 2021 at 13:06
• Personally, I find it presumptive of someone else to edit your answer to reorder the points (it would have been much more polite of that editor to engage in a discussion, as I have tried to do here), and I would be curious to know what evidence there is that the meta community here prefers "effort" over other kinds of context. Indeed, I see people constantly equating "context" to "an attempt", and complaining that such attempts are useless noise.
– Xander Henderson Mod
Sep 14, 2021 at 13:09
• @XanderHenderson well. :) I will try to figure out why I have "prejudice" against my own opinion...perhaps it is just the crossing of two streams that I have not yet reconciled in my own head Sep 14, 2021 at 13:13
• (also @XanderHenderson to be fair (and as you can see as a mod), in the lengthy deleted comments, the editor did engage in some discussion, but iirc I did not bring up this particular point on their edit) Sep 14, 2021 at 13:22
• Oi... I did not even look to see if there were deleted comments. :\ It is a shame that the discussion is now missing.
– Xander Henderson Mod
Sep 14, 2021 at 13:27
• To address a point raised here in the comments, I value "showing work" quite highly. Even just the slightest hint of what the asker has tried gives me a big clue to where their understanding on the problem broke down, and helps me to write an answer directed to their true misunderstanding. Sep 16, 2021 at 10:34
• @RyanG Because the comments were deleted, there was no indication that the edit had been a collaboration. I am leaving the comments here because it maintains the record, and clearly indicates that the edits were made collaboratively. Deleting the previous thread caused confusion.
– Xander Henderson Mod
Sep 21, 2021 at 15:10
• I like how this is presented, in a table. It's true that, that whole page, even thought just 2 parts of it are suggested to check (details and title), could be confusing? for a total new user. Perhaps this could be suggested to check instead of the other links. May 21 at 21:33
• @ryang done! thanks again for the suggestions. At this point I think you've put in more thought than I have. If I did something silly in the most recent edit feel free to fix it yourself. The last line was there because some people have asked on meta why they weren't getting an answer. But its not like the line was very informative by itself and should probably be dealt with more comprehensively elsewhere (some sort of "what is Math.SE" page?) Jun 28 at 4:21
• This table format is great! Kudos to all of you who created it. Jun 28 at 12:32
• Ideally, the Mathematics StackExchange homepage notifies users of the above table. @CalvinKhor I went in to add a bad-example title, and ended up making yet another round of edits, quite numerous! (If any change isn't preferable, please just revert it.) Jul 14 at 15:47
• I began looking at the changes groggy pre-coffee and antagonistic, but these are honestly good changes :) @ryang Jul 15 at 3:01
• @CalvinKhor Haha. A bit sheepish about still making edits a year on, so thanks for endorsing them. Really hoping that our table (it should be "frozen" by now, but then again, I've never been correct about this...) gets referred to even more frequently. Jul 15 at 4:43
• Welcome to Mathematics StackExchange! As this site is meant to be a useful repository rather than a Do My Homework forum, it's common courtesy to show what you've already tried, and really narrow down what you're struggling with. Most people here are glad to help once you've adequately motivated the problem. [Quick Guide](http://math.meta.stackexchange.com/a/34067/21813) to attracting answers and preventing your question from being deleted. Good luck!$\quad$ Please feel free to use/adapt this sample advisory. Jul 19 at 4:01
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2022-08-15 11:02:24
|
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|
http://openstudy.com/updates/4ff521bbe4b01c7be8c8436e
|
## anonymous 4 years ago hi what is the factor of 2x^2-3x-9?
1. lgbasallote
2x^2 - 3x - 9 break down the middle term 2x^2 + 6x - 3x - 9 group them (2x^2 + 6x) - (3x + 9) factor out 2x(x + 3) - 3(x+3) do you see it now?
2. anonymous
$x^2-3x-9=0$ $x^2-6x+3x-9=0$ $2x(x-3)+3(x-3)=0$ now you try to simplify.
3. anonymous
you can use the quadratic formula i.e $-b \pm \sqrt{b ^{2}-4ac}/2a$ here a=2 b=-3 c=-9 put the values of a, b and c in equation and you'll get your answer
4. anonymous
thanks for helping me
5. anonymous
factor of 2x+8
6. anonymous
28X+7
7. anonymous
we have to make the first term of these sums.
8. anonymous
I CANNOT SOLVE THAT ONE
9. anonymous
wait i am doing.
10. anonymous
hi what is the factor of 8x^3-216
11. anonymous
2x+342
12. anonymous
$First Term= (Middle Term)^2/4*(Last Term)$
13. anonymous
thanks,but im not asking what is the procedure im asking is what is the solution?
14. anonymous
kantutan
15. anonymous
gago ka talaga
16. anonymous
oo nga pala tuloy ung sa e nglish
17. anonymous
tar a abano Joke :D
18. anonymous
factor of 8x^3-216 $8x(x^2-27)=0$ $8x=0$ $x=0$ or $x^2-27=0$ $x^2=27$ $x=\sqrt{27}$
19. anonymous
abano add mo ko sa fwend m!!
20. anonymous
(x-6)(x+3)
21. anonymous
@danny_dumond Please don't post only answers as that's against the Code of Conduct: http://openstudy.com/code-of-conduct
22. anonymous
well find something like (cx+a) (dx+b) to = 2x^2-3x-9
23. anonymous
Gosh sorry! :P
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2016-12-03 11:39:14
|
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http://mathhelpforum.com/geometry/169537-equation-circle.html
|
Math Help - Equation of a circle?
1. Equation of a circle?
Find the equation of the circle which is tangent to all four of the circles characterized by these four equations:
x^2+y^2+10x=0
x^2+y^2-10x=0
x^2+y^2+10y=0
x^2+y^2-10y=0
???
2. If it's tangent to all four of the circles, then the derivatives will be equal at the points where they touch.
3. $x^2+y^2=100$ should be the required circle.
this is because the radius of each circle is 5 units and their centres are at (-5,0), (5,0), (0,5) and (0,-5).
if you draw a rough figure its easy to see that a symmetric flower shaped digram appears. and then its easy to find the required circle.
In general a circle tangent to four given circles will not exist. In this special symmetric situation it exists.
4. Originally Posted by Kaloda
Find the equation of the circle which is tangent to all four of the circles characterized by these four equations:
x^2+y^2+10x=0
x^2+y^2-10x=0
x^2+y^2+10y=0
x^2+y^2-10y=0
???
The graph of the 4 circles and the one tangent to them:
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2015-05-24 22:50:33
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https://therosebushblog.wordpress.com/
|
Punching Bag
I still love you even as you pound your fists in the only way you know how. I love you even though I am no more than a passing thought to you. I know you hurt. I know, because of the way you are hurting me. In every punch, I feel your soul, shaking. I feel your pain, and it is okay. I’m not bitter now, because I know you need this.
Some homes set sail
a little place called home
sails ashore
night skies and sunsets
people coming
and going
but always staying
the same
you
another place I once
called home
sitting by the water
below our feet
reflections of stories
of things untold
a love
so pure
so tender
we fear homes
like these
which move away
from our grasp
no trace
but tears
along the dock
she sits
looking down
reflections staring back
of memories
she knows
-she can’t go home
A letter unsent
I wish I could tell you how much missing you hurts. I wish I could tell you how much I need you right now. How I light a candle next to my bed, and imagine what it would be like to burn my skin. How I think about taking my car keys to my body as I’m driving past our spots. How much more I hate myself, now that you hate me too. I wish I could tell you these things. Maybe then you would listen. Maybe then you wouldn’t have left me all together and all at once.
tu me manques
*you are missing from me*
The day you left me.
It wasn’t the day we ended things, that I felt my heart shatter before me. This day, although saddening, was not the day I truly lost you. Today, my body aches because I know you are gone. The past few nights I fell back in my car, let the tears drift down my body, and slept as I drifted into the silence of my mind.
My Cloud
It’s been a while since I’ve written on here. I’d say it’s because I’ve been busy, being a college student and all. Although true, it is not the main culprit. I call this perpetrator, “my cloud.” It is grey and dull. It is exhausting and consuming. And although it appears quiet, do not be fooled, because it is a roaring thunder that strikes without mercy. It comes and goes like waves. It sends my hands scrambling through my hair, with hope that the weight of pressure might calm the storm. It sends my body to the cold touch of the wooden floor beside my bed. Anything is better than being in bed. I lie there, my face blank, with tears washing down my face. It is now quiet. The storm is taking a nap. I wish I too, could take a nap.
-depression
nature’s words
I feel different. I must see and hear things that other people don’t see and hear. The trees and the way they move with the wind, tell me stories. The flight of the birds give answers to my questions. The breeze reminds me to feel alive. The sunlight between the leaves lets me know she is always with me.
-Aunt Leslie
you aren’t alone
do you feel it the breeze outside your closed window
don’t worry i can feel it too
can you see it the world zipping by the traffic lights flashing from green to yellow to red glaring through your window
don’t worry i can see it too
can you hear it the silence in an immense crowd it’s like watching from a window as if you were never there
don’t worry i can hear it too
-you aren’t alone
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2019-03-24 17:39:28
|
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|
https://mathematica.stackexchange.com/questions/202243/how-to-solve-pde-with-periodic-and-anti-periodic-b-c/202287
|
# How to solve PDE with periodic and anti-periodic b.c.?
I need to solve the PDE for a complex function $$A(x,t)=A_r(x,t)+iA_i(x,t)$$
eq = D[A[x, t], t] + 1/4*Conjugate[A[x, t]]*A[x, t]^2 - D[A[x, t], {x, 2}] - 2*A[x, t] == 0;
over $$[-L,L]$$ and $$[0,t_\text{max}]$$. The equation is subject to a random initial condition and the boundary conditions as follows: $$A_r(-L,t)=A_r(L,t)$$ and $$A_i(-L,t)=-A_i(L,t)$$
L = 30; tmax = 30;
ini[x_] = 1/10*BSplineFunction[RandomReal[{-1, 1}, 20], SplineClosed -> True, SplineDegree -> 5][x/(2*L)];
ibcs = {Re[A[-L, t]] == Re[A[L, t]], Im[A[-L, t]] == -Im[A[L, t]], A[x, 0] == ini[x]};
Then, I solve it with NDSolve
sol = NDSolve[{eq, ibcs}, A, {x, -L, L}, {t, 0, tmax},
Method -> {"MethodOfLines",
"SpatialDiscretization" -> {"TensorProductGrid",
"MinPoints" -> 201, "MaxPoints" -> 201,
"DifferenceOrder" -> "Pseudospectral"}}, AccuracyGoal -> 20]
NDSolve::bcedge: Boundary condition Im[A[-30,t]]==-Im[A[30,t]] is not specified on a single edge of the boundary of the computational domain.>>
I didn't understand the error. Why the boundary conditions (bcs) must be specified on a single edge. Should not we set the bcs at both sides? Any suggestion is highly appreciated.
Thank for @xzczd's comment:
I just knew that NDSolve could not handle anti-periodic bc. Yes, the equation can be solved with a periodic bc:
periodbcs = {A[-L, t] == A[L, t], A[x, 0] == ini[x]}
But the solution should be incorrect because the solution is a real function by observing its imaginary part.
ContourPlot[Evaluate[Im[A[x, t] /. sol]], {x, -L, L}, {t, 0, tmax},
Contours -> 10, PlotRange -> All, PlotLegends -> Automatic,
ColorFunction -> Hue, FrameLabel -> {"x", "t"}, PlotLabel -> "Ai", ImageSize -> 200]
Response to @user64494's comment:
Yes, I can split the real and imaginary parts by writing the 2nd term as
$$(A^\ast A)A=\vert A\vert^2A=(A_r^2+A_i^2)(A_r+i A_i)=A_r^3+A_i^2A_r+i(A_r^2A_i+A_i^3)$$
Then the equation can be split into
eqs = {D[Ar[x, t], t] + 1/4*(Ar[x, t]^3+Ai[x, t]^2*Ar[x, t]) - D[Ar[x, t], {x, 2}] - 2*Ar[x, t] == 0,
D[Ai[x, t], t] + 1/4*(Ai[x, t]^3+Ar[x, t]^2*Ai[x, t]) - D[Ai[x, t], {x, 2}] - 2*Ai[x, t] == 0};
But I don't know how to make an anti-periodic initial condition (Ai[x, 0] = inianti[x]) to be consistent with the boundary condition.
ibcs = {Ar[-L, t] == Ar[L, t], Ai[-L, t] == -Ai[L, t], Ar[x, 0] == ini[x], Ai[x, 0] = inianti[x]};
• @xzczd many thanks. Please see my update, where I can explain more clearly. Any workaround will be highly appreciated! – Nobody Jul 17 at 15:59
• Is it possible to split the real and imaginary parts in eq and ibcs? – user64494 Jul 17 at 16:27
• @user64494 great idea. Please see my update. Any suggestion :) – Nobody Jul 17 at 16:48
• Did you try to solve the split problem? – user64494 Jul 17 at 16:56
• I haven’t because I don’t know how to get a random anti-periodic initial condition. Please help. – Nobody Jul 17 at 16:59
# Pre-v12 Solution
The approach here is fully applicable to your problem. Anyway, the corresponding coding isn't trivial, so let me give an answer.
We start from the splitted equation system because Re, Im, Conjugate isn't that convenient for subsequent coding. The form of b.c.s are slightly modified, because both periodic b.c. and anti-periodic b.c. are set with one-sided difference formula in this method (which is different from using PeriodicInterpolation of NDSolveFiniteDifferenceDerivative) and we need 4 constraints in x direction in total:
Clear[ini, inianti, Ai]
eqs = {D[Ar[x, t], t] + 1/4 (Ar[x, t]^3 + Ai[x, t]^2 Ar[x, t]) - D[Ar[x, t], {x, 2}] -
2 Ar[x, t] == 0,
D[Ai[x, t], t] + 1/4 (Ai[x, t]^3 + Ar[x, t]^2 Ai[x, t]) - D[Ai[x, t], {x, 2}] -
2 Ai[x, t] == 0};
ic = {Ar[x, 0] == ini[x], Ai[x, 0] == inianti[x]};
bc = {Ar[-L, t] == Ar[L, t], Ai[-L, t] == -Ai[L, t],
Derivative[1, 0][Ar][-L, t] == Derivative[1, 0][Ar][L, t],
Derivative[1, 0][Ai][-L, t] == -Derivative[1, 0][Ai][L, t]};
# Remark
Derivative[1, 0][Ar][-L, t] == Derivative[1, 0][Ar][L, t] is added because periodic b.c. implies the solution is smooth enough across the boundary, but frankly speaking, I'm not familiar with anti-periodic b.c. and not sure if Derivative[1, 0][Ai][-L, t] == -Derivative[1, 0][Ai][L, t] is correct, but do remember a supplement for derivative of x of Ai at the boundary is necessary, or a particular solution won't be determined.
The i.c.s are simply generated randomly, they don't satisfy the b.c.s of course, but this should not be a big deal because the i.c.s will be slightly modified at the boundary to satisfy the b.c.s in the upcoming disretization step. (For more information about handling inconsistency between i.c. and b.c., you may want to check this post. )
L = 30; tmax = 30;
SeedRandom[1];
ini = ListInterpolation[RandomReal[{-1, 1}, 20], {{-L, L}}];
inianti = ListInterpolation[RandomReal[{-1, 1}, 20], {{-L, L}}];
Finally, discretize the PDE system to an ODE system and solve, with the help of pdetoode:
points = 200; domain = {-L, L}; difforder = 4;
grid = Array[# &, points, domain];
(* Definition of pdetoode isn't included in this code piece,
ptoofunc = pdetoode[{Ar, Ai}[x, t], t, grid, difforder];
odebc = Map[ptoofunc, bc, {2}]
del = #[[2 ;; -2]] &;
odeic = del /@ ptoofunc@ic;
ode = del /@ ptoofunc@eqs;
sollst = NDSolveValue[{ode, odeic, odebc},
Table[v[x], {v, {Ar, Ai}}, {x, grid}], {t, 0, tmax}];
{solAr, solAi} = rebuild[#, grid, -1] & /@ sollst;
Check:
Plot[{solAr[-L, t], solAr[L, t], solAi[-L, t], solAi[L, t]}, {t, 0, tmax},
PlotStyle -> {Automatic, {Thick, Red, Dashed}, Dotted, Dotted}]
With[{d = Derivative[1, 0]},
Plot[{d[solAr][-L, t], d[solAr][L, t], d[solAi][-L, t], d[solAi][L, t]}, {t, 0, 2},
PlotStyle -> {Automatic, {Thick, Red, Dashed}, Dotted, Dotted}, PlotRange -> All]]
# Suspicious v12 Solution
Since v12, "FiniteElement" method can handle nonlinear PDE, so it's possible to solve the problem with PeriodicBoundaryCondition in principle. Nevertheless, the v12 solution is suspicious:
test = NDSolveValue[{eqs, ic,
PeriodicBoundaryCondition[Ar[x, t], x == L, Function[x, x - 2 L]],
PeriodicBoundaryCondition[-Ai[x, t], x == L, Function[x, x - 2 L]]}, {Ar, Ai}, {t,
0, tmax}, {x, -L, L},
Method -> {"MethodOfLines",
"SpatialDiscretization" -> {"FiniteElement",
"MeshOptions" -> "MaxCellMeasure" -> 0.01}}]; // AbsoluteTiming
With[{d = Derivative[1, 0]},
Plot[{d[test[[1]]][-L, t], d[test[[1]]][L, t], d[test[[2]]][-L, t],
d[test[[2]]][L, t]}, {t, 0, 2},
PlotStyle -> {Automatic, {Thick, Red, Dashed}, Dotted, Dotted}, PlotRange -> All]]
It's clear Derivative[1, 0][Ar][-L, t] == Derivative[1, 0][Ar][L, t] isn't satisfied. (Zero NeumannValue is set at $$x=-L$$? ) I guess the underlying issue may be related to that in this post.
• Thank you very much @xzczd. I noticed that you didn't write a semicolon at the end of odebc = Map[ptoofunc, bc, {2}] on purpose to show me why you Map at level 2 :) Thanks! – Nobody Jul 18 at 11:03
• a question: in eqs you defined the sequence of independent vars as [x,t], why does in the solution, say, solAr[t, -L], the sequence become [t,x]? – Nobody Jul 18 at 11:16
• @Nobody By default, the first variable of the function generated by rebuild is the variable amounts to time, if you want the original order, use e.g. {solAr, solAi} = rebuild[#, grid, 2] & /@ sollst. – xzczd Jul 18 at 11:50
• @Nobody Oops, I've made a mistake in my original check, and the original points` turns out to be too small. Corrected. – xzczd Jul 18 at 12:10
• why did you say that the original result was incorrect? How did you identify that the problem results from the low mesh resolution? Thank you! – Nobody Jul 18 at 14:50
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2019-10-15 17:48:19
|
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|
http://www.webdeveloper.com/forum/showthread.php?362923-xmlHttpRequest-not-working-for-email-script&s=f27ad15e252e88c5bd834cc30630876e&p=1503427
|
# Thread: xmlHttpRequest not working for email script
1. Registered User
Join Date
Apr 2017
Posts
4
## xmlHttpRequest not working for email script
I'm trying to pull a msg file from the server to display in a basic email reader script so Outlook isn't needed. I'm struggling every which way. The console log says there's no JavaScript on the page... even though the script type='text/javascript'. I just get a blank page with no errors!
Code:
var message;
console.log('Testing console');
function httpGetAsync(theUrl, callback){
var xmlHttp = new XMLHttpRequest();
if (xmlHttp.readyState == 4 && xmlHttp.status == 200)
callback(xmlHttp.responseText);
message = xmlHttp.responseText;
}
xmlHttp.open("GET", theUrl, true); // true for asynchronous
xmlHttp.send(null);
}
httpGetAsync('\Test.txt', function(resp) { \\tried 'Test.txt' also... really need to be able to input 'z:\whole\path\to\test.txt'
console.log(resp);
});
//This part is email reader that works with 3 other external scripts
function isSupportedFileAPI() {
return window.File && window.FileReader && window.FileList && window.Blob;
}
function formatEmail(data) {
return data.name ? data.name + " [" + data.email + "]" : data.email;
}
$(function () { if (isSupportedFileAPI()) {$('.src-file').change(function () {
var selectedFile = message; //removed Browse button... this.files[0];
if (!selectedFile) {
$('.msg-info, .incorrect-type').hide(); return; } if (selectedFile.name.indexOf('.msg') == -1) {$('.msg-info').hide();
$('.incorrect-type').show(); return; }$('.msg-example .msg-file-name').html(selectedFile.name);
$('.incorrect-type').hide(); // read file... var fileReader = new FileReader(); fileReader.onload = function (evt) { var buffer = evt.target.result; var msgReader = new MSGReader(buffer); var fileData = msgReader.getFileData(); if (!fileData.error) {$('.msg-example .msg-from').html(formatEmail({name: fileData.senderName, email: fileData.senderEmail}));
$('.msg-example .msg-to').html(jQuery.map(fileData.recipients, function (recipient, i) { return formatEmail(recipient); }).join('<br/>'));$('.msg-example .msg-subject').html(fileData.subject);
$('.msg-example .msg-body').html( fileData.body ? fileData.body.substring(0, Math.min(500, fileData.body.length)) + (fileData.body.length > 500 ? '...' : '') : '');$('.msg-example .msg-attachment').html(jQuery.map(fileData.attachments, function (attachment, i) {
return attachment.fileName + ' [' + attachment.contentLength + 'bytes]' +
(attachment.pidContentId ? '; ID = ' + attachment.pidContentId : '');
}).join('<br/>'));
$('.msg-info').show(); // Use msgReader.getAttachment to access attachment content ... // msgReader.getAttachment(0) or msgReader.getAttachment(fileData.attachments[0]) } else {$('.msg-info').hide();
$('.incorrect-type').show(); } }; fileReader.readAsArrayBuffer(selectedFile); }); } else {$('.msg-example').hide();
\$('.file-api-not-available').show();
}
});
2. You do not "GET" when posting a form, you "POST" the form and you have to use the command xmlhttp.send( null ) because you are saying send nothing and the form needs to send data for it to work and you don't need any JQuery to get or for fomatting the email, you cn do that on the server, just get the raw data to the server, validate it and then send it in an email. The form data needs to be passed as a parameter because yu won't be getting data to the server, you use something like xmlhttp.send( document.forms.yourFormName ) you can pass the form object itself. you also have to set the correct enctype attribute in HTML form element, again you need a web form to do this and if you don't have a web form element then this is another problem to resolve as well.
3. Registered User
Join Date
Apr 2017
Posts
4
Remember remember and thank you for your reply \\.\, however it's not an email form. There are pdf and msg files on the server that are correspondence or information about a project. I'm able to display the pdf's quite easily, but I'm having a problem with the msg files. I found a msg reader script, and since it runs on the client it seems to me there would need to be a call to the server, basically a clickable icon link... to GET the file via xmlHTTPrequest, then display it using the basic reader script so Outlook isn't needed. The basic email reader script was made use of a Browse button to find the msg file. I can't use that of course, because the msg file is on the server. I've tried a number of ways... in the example above, I had tried assigning it with var selectedFile = message; but it just displays blankness with no error.
4. Registered User
Join Date
Apr 2017
Posts
5
Hi, the first thing i see that maybe you use "Internet Explorer" and are not solving the XDomainRequest problem?
If it's not that, then you could use "Chrome" (for example) and check your site with it's "developer tools". There you'll find error messages and further options to test your site.
Hope that helps...
5. Registered User
Join Date
Apr 2017
Posts
5
did you include jQuery?
6. Registered User
Join Date
Apr 2017
Posts
5
Originally Posted by mirkov
Hi, the first thing i see that maybe you use "Internet Explorer" and are not solving the XDomainRequest problem?
Sorry, forget that part... i'm actually, probably pretty tired. :-) jQuery makes the AJAX-call happen...
but i would maybe find a full app that works out of the box.. instead of trying to fix something that doesn't... (just in case you didn't write it yourself)
Cheers
7. Registered User
Join Date
Apr 2017
Posts
4
## Nowhere Fast
I'm mostly testing in Firefox, sometimes Chrome... less often IE. This is as close to "out of the box" as I could find. I've tested the email reader on the client side and it works fine. It seems to be mostly a matter of getting an xmlHTTPRequest to pull a file from the Server instead of using a Browse button to find a file on the local machine... because I'm eliminating the Browse button entirely. I tried outputting xmlHTTPRequest to message; then assigned var selectedFile = message; but it gets me a blank page with no errors.
8. Registered User
Join Date
Apr 2017
Posts
4
I've got xmlHTTPRequest working... it was a network error issue, but I get a 404 page now when I try to display .msg file. The file is there, because I can change the extension to .txt and it will display jibberish... (maybe I'm there, and it just needs to be plugged into the reader script somewhere?) Besides that, I thought if I used overrideMimType it would help, but it displays [object blob].
There are currently 1 users browsing this thread. (0 members and 1 guests)
#### Posting Permissions
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## X vBulletin 4.2.2 Debug Information
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2018-01-18 08:15:47
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|
https://www.simis.io/docs/atmosphere-turbulent-wind
|
# Turbulent wind
Ashes is able to read to types of turbulent wind files:
• .wnd files generated with TurbSim
• .bin files generated by the Mann turbulence simulator
There are conceptual differences between these two types, which are explained in the Turbulence section of the Theory Manual.
TurbSim can be found on the NREL website at https://nwtc.nrel.gov/TurbSim (accessed Jan 2019), but is also shipped with Ashes. It is thus possible to generate turbulent wind files within Ashes, using the Turbulent wind tool.
The Mann turbulence simulator can be downloaded from the HAWC2 website at http://www.hawc2.dk/download/pre-processing-tools (accessed jan 2019). It is also shipped with Ashes but is currently only integrated into the batch tool. For use in Time simulation, you'll have to create the turbulent wind field with the Mann turbulence simulator itself and load the files, as explained below.
To see how to generate turbulent wind fields, seeTurbulent Wind Creator. Once the turbulent wind field has been created, either with TurbSim or with the Mann turbulence generator, it can be chosen from the Wind file parameter shown in the following section.1. Clicking on the Turbulent wind field parameter will open a dialog that enables you to browse to the folder where the turbulent wind fields are located. The figure below shows the dialog that enables you to select the turbulent wind field.
The parameters that can be modified in the turbulent wind part are listed below
## Source
### Source
Select if you want the turbulent wind field to be read from file or generated by Ashes.
Options:
From parameters (default):
The turbulent wind field is generated by Ashes based on the entered parameters.
From file:
The turbulent wind field is read from file.
### Turbulent wind file
Choose the file that contains the turbulent wind field. The format must be either
1) TurbSim .wnd, or
2) Mann turbulence generator (also called the IEC Turbulence Simulator) .txt format (which must link to three .bin files).
Turbulent wind fields can be created with the Turbulent wind tool.
If no file is chosen, the wind speed is 0. Clicking this field will open the dialog shown in the picture above.
Note that if you select a turbulent wind field created with TurbSim, the wind speed, wind angle and turbulence intensity is already defined and cannot be changed in the parameter list. These parameters can only be selected for turbulent wind fields created with the Mann turbulence generator.
• Default value:
• Unit:
## Wind general
### Average angle
The average angle (direction) of the wind in the horizontal plane relative to North. Clockwise is positive. 0° means that the wind is coming from the North. 90° means that the wind is coming from the East.Note that this is only used for Mann turbulent winds.
• Default value: 0
• Unit: $°$
• Range: -360 — 360
### Average wind speed
The average wind speed in the turbulent wind field. Note that this is only used for Mann turbulent winds.
• Default value: 12
• Unit: ${\text{m}} \over {\text{s}}$
• Range: 0 — 1e+08
### Shear
Decides if a shear law is applied to the deterministic wind.
• Default value: False
• Unit:
### Power law exponent
The shear is computed using a power law. This is the power law exponent.
To see how the power law is computed, see Wind profile power law
• Default value: 0.2
• Unit:
• Range: 0 — 100
## Grid dimensions
### Grid shape
The shape of the turbulent wind grid. Either rectangular or square.
Options:
Square (default):
A square shaped turbulent wind grid.
Rectangular:
A rectangular shaped turbulent wind grid.
### Base turbulence grid on model?
Check this parameter to make the turbulent wind grid based on the current model.
• Default value: True
• Unit:
### Reference height scheme
This parameter lets your define whether the point of application of the reference speed (used to compute a vertical wind shear) is input by you or defined as the hub height. This parameter is only relevant if a shear law is applied to the wind.
IHub height is selected, the reference wind speed for the shear will be applied at hub height. If the turbine has multiple rotors, the reference wind speed will be applied at the average hub height. If there is no rotor, the reference speed is applied at the average height of the nodes at sea level.
Options:
Hub height (default):
The reference height is set to the hub height.
User defined:
The reference height is set explicitly by the user (you).
### Reference height
The height above the ground (or above sea level for offshore turbine) where the reference wind speed is applied.
Hub height is often used for the reference height, but in some cases it is convenient to use another height. E.g. if the wind speed is given for a height of 10 m above ground, then this parameter should be set to 10 m. Note: The reference height only has an influence if there is shear (see Wind profile power law)
• Default value: 10
• Unit: $\text{m}$
• Range: 0.01 — 1000
### Width of the turbulence grid
The width of the turbulent wind field.
• Default value: 100
• Unit: $\text{m}$
• Range: -1e+07 — 1e+08
### Height of the turbulence grid
The height of the turbulent wind grid.
• Default value: 100
• Unit: $\text{m}$
• Range: -1e+07 — 1e+08
### Size factor
Determines the size of the turbulence field. For instance, a factor of 2 will generate a field that is twice the width and height of the rotor diameter. The recommended value for onshore turbines is 1.1, while offshore turbines might require larger fields if they are subjected to large displacements and rotations.
• Default value: 1.1
• Unit:
• Range: 1 — 1000
### Horizontal size factor
Determines the size of the turbulence field in horizontal direction. For instance, a factor of 2 will generate a field that is twice the width and height of the rotor diameter. The recommended value for onshore turbines is 1.1, while offshore turbines might require larger fields if they are subjected to large displacements and rotations.
• Default value: 1.1
• Unit:
• Range: 1 — 1000
### Vertical size factor
Determines the size of the turbulence field in vertical direction. For instance, a factor of 2 will generate a field that is twice the width and height of the rotor diameter. The recommended value for onshore turbines is 1.1, while offshore turbines might require larger fields if they are subjected to large displacements and rotations.
• Default value: 1.1
• Unit:
• Range: 1 — 1000
### Grid resolution
The grid resolution type. The turbulent wind grid can either defined by the number of points or by the distances between the points.
Options:
By grid distance:
The number of points is derived by the distance between the points.
By grid points (default):
The distance between the points is defined by the number of points.
### Horizontal grid points
The number of grid points of the turbulent wind field in horizontal direction.
• Default value: 32
• Unit:
• Range: 0 — 64
### Vertical grid points
The number of grid points of the turbulent wind field in vertical direction.
• Default value: 32
• Unit:
• Range: 0 — 64
### Horizontal grid distance
The minimum distance between grid points in the turbulence field in horizontal direction. The Turbsim documentation recommends a value equal to the mean chord of the blade. However, the memory requirement of TurbSim scales as the fourth power of the number of grid points, so a very fine-meshed grid for large offshore turbines might not be feasible.
• Default value: 5
• Unit: $\text{m}$
• Range: -1e+30 — 1e+23
### Vertical grid distance
The minimum distance between grid points in the turbulence field in vertical direction. The TurbSim documentation recommends a value equal to the mean chord of the blade. However, the memory requirement of TurbSim scales as the fourth power of the number of grid points, so a very fine-meshed grid for large offshore turbines might not be feasible.
• Default value: 5
• Unit: $\text{m}$
• Range: -1e+30 — 1e+23
## Turbulence
### Turbulence model
Select which turbulence model should be used to generate the turbulent wind field.
Options:
IEC Kaimal model (NTM) (default):
Use the IEC Kaimal model.
IEC Kaimal extreme turbulence (ETM):
Use the IEC Kaimal extreme turbulence (ETM) model.
Von Karman model (IECVKM):
Use the IEC Von Karman model.
Mann turbulence:
Use the Mann turbulence model.
### Turbulence intensity category
The turbulence intensity category as defined in IEC 61400-1.
Options:
A (default):
The turbulence intensity Iref is set to 0.16.
B:
The turbulence intensity Iref is set to 0.14.
C:
The turbulence intensity Iref is set to 0.12.
User defined:
The turbulence intensity is defined by you.
### Turbulence intensity
The expected value of the turbulence intensity at 15 m/s (in percent), i.e. Iref in IEC 61400-1. A typical interval for turbulence intensity is 10-20%.
• Default value: 16
• Unit: $\text{%}$
• Range: 0 — 100
### IEC turbine class
The IEC turbine class.
Options:
I (default):
IEC turbine class I
Annual mean wind speed: 10 m/s
50-year extreme wind speed over 10 minutes: 50 m/s
50-year extreme gust over 3 seconds: 70 m/s
II:
IEC turbine class II
Annual mean wind speed: 8.5 m/s
50-year extreme wind speed over 10 minutes: 42.5 m/s
50-year extreme gust over 3 seconds: 59.5 m/s
III:
IEC turbine class III
Annual mean wind speed: 7.5 m/s
50-year extreme wind speed over 10 minutes: 37.5 m/s
50-year extreme gust over 3 seconds: 52.5 m/s
### Alfa times epsilon
This parameters scales the intensity of the turbulence. For further explanation the user is refered to the manual of the Mann turbuelnce generator.
• Default value: 1
• Unit:
• Range: 0 — 100
### L
The L variable in the Mann turbulence model, corresponding to 0.7-0.8 Λ in IEC61400-1 ed3.
• Default value: 29.4
• Unit:
• Range: 0 — 100
### Gamma
Gamma variable in the Mann turbulence model.
• Default value: 3
• Unit:
• Range: 0 — 100
## Simulation
### Seed scheme
Select if you want to enter the seed of the turbulent wind field manually or if it should be randomly generated by Ashes.
Options:
Random (default):
The seed is randomly set based on the current time.
User defined:
You enter the random seed.
### Seed
The random seed of the turbulent wind field. Defines the randomness of the internally generated numbers. Using the same random seed twice will give the exactly same turbulent wind field.
• Default value: 1
• Unit:
• Range: 1 — 1e+08
### High frequency compensation
No description yet
• Default value: True
• Unit:
### Time step scheme
Defines if the time step for turbulent wind should be the same as for the FEM analysis or be user defined.
Options:
Use FEM analysis time step (default):
Use same time step as in FEM analysis.
User defined:
You define the time step.
### Turbulence time step
Time step of the turbulent wind field.
• Default value: 0.03
• Unit: $\text{s}$
• Range: 0 — 1e+06
## Flow angles
### Vertical mean flow angle
The angle of the mean flow in vertical direction.
• Default value: 0
• Unit: $°$
• Range: -90 — 90
### Horizontal mean flow angle
Mean flow angle of the turbulent wind field in horizontal direction relative to North.
• Default value: 0
• Unit: $°$
• Range: -360 — 360
|
2023-03-26 16:02:30
|
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|
http://www.ck12.org/book/Basic-Probability-and-Statistics-A-Full-Course/section/7.0/
|
<meta http-equiv="refresh" content="1; url=/nojavascript/">
You are reading an older version of this FlexBook® textbook: CK-12 Basic Probability and Statistics Go to the latest version.
# Chapter 7: Organizing and Displaying Distributions of Data
Difficulty Level: Basic Created by: CK-12
Introduction
The local arena is trying to attract as many participants as possible to attend the community’s “Skate for Scoliosis” event. Participants pay a fee of $10.00 for registering, and, in addition, the arena will donate$3.00 for each hour a participant skates, up to a maximum of 6 hours. Create a table of values and draw a graph to represent a participant who skates for the entire 6 hours. How much money can a participant raise for the community if he/she skates for the maximum length of time?
This problem will be revisited later in the chapter.
When data is collected from surveys or experiments, it is often displayed in charts, tables, or graphs in order to produce a visual image that is helpful in interpreting the results. From a graph or table, an observer is able to detect any patterns or trends that may exist. The most common graphs that are used in statistics are line graphs, scatter plots, bar graphs, histograms, frequency polygons, pie charts, and box-and-whisker plots.
Basic
Feb 23, 2012
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2015-09-04 21:10:48
|
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|
https://blender.stackexchange.com/questions/72691/sort-a-list-of-objects-by-their-distance-from-a-point
|
# Sort a list of objects by their distance from a point
I have a list of objects like this [bpy.data.objects["Text.002], bpy.data.objects["Text.003], bpy.data.objects["Text.005], bpy.data.objects["Text.007]] how can I sort them by their distance from a point like for example p =(0, 0, 0)?
I've tried to calculate the distance from two points in the 3d space using the origin and the point coordinates, but then how can I sort the objects?
There are a number of ways to sort lists in python. Here is one using lambda.
import bpy
from mathutils import Vector
# some list of objects (taken from q)
objects = [bpy.data.objects["Text.002"],
bpy.data.objects["Text.003"],
bpy.data.objects["Text.005"],
bpy.data.objects["Text.007"]]
# sort by location from (0, 0, 0)
objects.sort(key=lambda o: o.location.length)
# sort by visual location from (0, 0, 0)
# eg objects moved by constraint / parenting etc.
objects.sort(key=lambda o:
o.matrix_world.to_translation().length)
v = Vector((1, 2, 3))
# sort by distance from v
objects.sort(key=lambda o:
(o.matrix_world.to_translation() - v).length)
|
2020-01-25 11:52:41
|
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|
http://mathhelpforum.com/pre-calculus/83839-how-find-roots.html
|
Thread: How to find roots
1. How to find roots
Please i need to solve this cubic equation step by step. I need to find roots, C and D are constants
x^3-x^2+Cx-D=0
2. Originally Posted by chemtoli
Please i need to solve this cubic equation step by step. I need to find roots, C and D are constants
x^3-x^2+Cx-D=0
Read this: The "Cubic Formula"
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2017-08-20 08:52:38
|
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https://www.math.uni-potsdam.de/institut/veranstaltungen/archiv/details-archiv/veranstaltungsdetails/characteristic-classes-implemented-in-sagemath
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# Characteristic Classes implemented in SageMath
#### 22.05. bis 22.05.2019, 4:00 - 4:30 pm – Haus 9, Raum 2.22
Michael Jung
SageMath is an open source variant of Mathematica and useful in various areas in mathematics. For my master thesis, I implement characteristic classes of vector bundles using the Chern--Weil homomorphism. Characteristic classes can describe the twistedness of a vector bundle and are important ingredients of the Atiyah--Singer index theorem. Given a vector bundle E->M over a differentiable manifold M, it is possible to construct any real (or complex) characteristic class (like the Euler class) out of some connection matrix given on E. In this talk I will shortly introduce characteristic classes and explain the algorithm. If there is some time, I will present a demo notebook of my current progress in SageMath.
zu den Veranstaltungen
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2023-01-28 17:49:49
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https://study.com/academy/answer/satellite-a-orbits-a-planet-with-a-speed-of-10-000-m-s-satellite-b-is-twice-as-massive-as-satellite-a-and-orbits-at-twice-the-distance-from-the-center-of-the-planet-what-is-satellite-b-s-speed.html
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# Satellite A orbits a planet with a speed of 10,000 m/s. Satellite B is twice as massive as...
## Question:
Satellite A orbits a planet with a speed of 10,000 m/s. Satellite B is twice as massive as satellite A and orbits at twice the distance from the center of the planet. What is Satellite B's speed?
## Force balance equations in Satellite Motion:
Assuming that the satellite is moving in a circular orbit, we can easily write the gravitational force acting between the Earth and the Satellite. Since the Satellite is changing its direction of motion, the satellite is accelerating. This makes the Satellite a non-inertial frame of reference. Thus for our convenience of study, we can represent the force on the Satellite as
{eq}F=m\dfrac{v^{2}}{r} {/eq}
where m is the mass of the Satellite, r is the distance between the Satellite and the Earth. And this force is generated by Gravitation. Thus
{eq}G\dfrac{Mm}{r^{2}}=m\dfrac{v^{2}}{r} {/eq}
or more simply, we can write
{eq}G\dfrac{M}{r}=v^{2} {/eq}
A better expression would be
{eq}v^{2}r=\text{constant} {/eq}
This expression is a direct result that comes from Kepler's 2nd Laws of Planetary Motion which states that the areal velocity of a body orbiting a planet remains constant. This result is further extended to show how angular momentum in planetary motion remains conserved.
It should be clear from the above expression, that the orbital velocity of a satellite is independent of its mass.
Let the initial orbital radius be {eq}r_{\circ} \\ v_{\circ}=10000 \ ms^{-1} {/eq}
The orbital radius for the second satellite is
{eq}r'=2r_{\circ} {/eq}
Therefore
{eq}(10000)^{2}r_{\circ}=v^{2}(2r_{\circ})\\ v=\dfrac{10000}{\sqrt{2}}\\ v=7071.06 \ ms^{-1} {/eq}
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2020-01-25 02:39:05
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http://www.conservapedia.com/Essay:Quantifying_Liberal_Style
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# Essay:Quantifying Liberal Style
Statistical methods have been used to quantify a wide range of characteristics of writing. For example, the Fleisch-Kincaid grade level and reading ease scores may be computed by almost any word processor, including many versions of Microsoft Word. These scores attempt to assess the level of sophistication of samples of writing, and have been used to give concrete evidence of a dumbing-down of presidential inaugural addresses over time. Great Britain is even considering implementing computerized grading of essays on some standardized tests. Given the objective nature of many of the characteristics of liberal style identified at Conservapedia, it is natural to devise analogous measures of the degree of liberal style of a specimen of writing.
A rough formula to measure the liberal style of an editor, adapted to Wiki-style websites, is
$\textrm{Liberality} = C_0 \cdot \frac{\textrm{TalkPst}}{\textrm{MainPst}} + C_1 \cdot \frac{\textrm{TalkWd}}{\textrm{TalkPst}} + C_2 \cdot \left( \frac{\lambda \cdot \textrm{LibWd} - \textrm{ConWd}}{\textrm{MainPst}+\textrm{TalkPst}} \right) + C_3 \,\left( \frac{\textrm{LibPhr}}{\textrm{MainPst}+\textrm{TalkPst}} \right)^2 + C_4 \, \sqrt{\textrm{LastWdProp}-\frac{1}{2}}$,
where:
• MainPst = number of posts to mainspace pages.
• TalkPst = number of posts to talk pages.
• TalkWd = number of words posted to talk pages.
• LibWd = number of uses of liberal words from reference list
• ConWd = number of uses of conservative words from reference list
• λ = (number of conservative words in reference list)/(number of liberal words in reference list).
• LibPhr = number of uses of liberal favorite phrases identified in Liberal style, such as "silence speaks volumes" and "reflects poorly on the site"
• LastWdProp = proportion of Talk page discussions in which a user makes the last post in a section (i.e., == ... ==). Values greater than 1/2 indicate a tendency towards last-wordism. When the value inside the square root is negative this should be understood as 0. N.B.: since this number is less than 1, taking the square root serves to increase the penalty.
Additionally, the Ci are constants which must be determined through careful testing. For now, we assume that C0 = 35, C1 = 1, C2 = 150, C3 = 300, C4 = 500. The final score as well as all of the constants are unitless, and the values simply reflect a scale of liberalism rather than an estimate of thoughts/word.
The quantification of liberal style has an astonishing array of possible applications. Most directly, it may be applied to the automatic detection of vandals on Conservapedia who attempt to insert liberal bias undetected. Related indices of liberal bias (not based on a Wiki-style count) could also be used to measure the degree to which various Bible translations have been compromised by liberal bias, and for quality control on books in the Conservative Bible Project. Indeed, linguistic indicators such as vocabulary use have long been used by scholars to gauge he authenticity of various ancient texts (including the Bible), and applying a similar metric (adapted to other languages) to the original text of the Bible may help discover additional passages which are late additions. Measures of liberal style may also be applied to measure the political bias of various news outlets, and of specific anchors at those outlets. Additionally, they may be used to gauge the true beliefs of political figures, who often pretend to be more conservative than they really are in order to win in Republican primaries.
While some have questioned the usefulness of quantifying things like open-mindedness and liberal style (see point 30 on Liberal style), the success of similar metrics for other aspects of language indicates that such calculations are indeed very meaningful.
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2014-09-01 21:08:02
|
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http://www.mediawiki.org/wiki/Manual:Enable_TeX/problems
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# Manual:Enable TeX/problems
Many users reported problems with installation of texvc.
There are 2 groups of such problems:
• it doesn't work even from the command line
• it does work from the command line, but not from PHP
• So how does one fix this if it works on the command line and not in PHP (errors like: Failed to parse (unknown error):"
### Command line
You need to install with PS support (ImageMagick is not nice to compile by hand, get binaries if you can) or Ghostscript, Latex, dvips (part of Latex).
If you do, check permissions.
Comment file unlinking out in render.ml to see what's going on better.
strace or equivalent utility may be useful for tracing command executions.
You need GNU make to compile texvc. On some non-Linux Unices it's under name gmake instead of make.
### PHP
Check that it works from the command line. If not, see the previous section.
The environment under Apache/PHP is different that the shell. Typical problems:
• user may be different; check permissions.
• PATH variable may be different; use absolute paths in render.ml if you can't fix it.
• you may be in a jail/chroot.
### Error : Failed to parse (Missing texvc executable)
That error is returned in response to this test:
if( function_exists( 'is_executable' ) && !is_executable( $wgTexvc ) ) { return$this->_error( 'math_notexvc' );
}
So, if you're getting the error there are a few possibilities:
• $wgTexvc is set to the wrong path • the file doesn't exist • the file isn't executable by the web server according to permissions • some weird PHP restriction is preventing you from accessing the file • If running on Windows, you may need to install Cygwin and ensure that SH is on the PATH. You should check into all of these possibilities. If you are running selinux, it may be denying permission to httpd to execute the file. See the selinux section below. Another possibility is that you wrote that wiki page before compiling texvc, and haven't rerendered any math since. Remember that page renderings are aggressively cached; run your tests in a preview and try varying texts. Someone managed to fix it by "by uninstalling the Suse native apache, mysql, php, and mediawiki, and replacing them with xampp and mediawiki tarball.". He has no idea why it worked. Another dirty fix if you are absolutely sure things should be working and this is causing the problem, is commenting the return line and replacing it by a dummy as in # return$this->_error( 'math_notexvc' );
$cmd = "foo"; which bypasses the check and goes ahead running the command. If you are running AppArmor (Suse 10 does this by default) add texvc to the AppArmor Profile, this can most easily be done via yast2. Be sure to enable execute rights ("x") in the editor, otherwise AppArmor will block the execution of texvc. If AppArmor is blocking an application usually it is logged in /var/log/apparmor. ### Error : Failed to parse (PNG conversion failed; check for correct installation of latex, dvips, gs, and convert) This is the most severe error. It indicates, that the directories with the programs mentioned are not reachable for the texvc program. If you see these commands at command line with commands which latex which dvips which gs which convert then, perhaps, nothing can be done: this software is not compatible with your server. If you are running selinux, it may be preventing the parse. See the Selinux section below. I got the same errormessage and which latex, which dvips, etc all showed that the necessary binaries where in the path. After running "fmtutil-sys --all" once on the commandline of the server (as root) it worked. So maybe you wan't to try this also. A cause of this is that texvc cannot see a latex.fmt file. This lives in various places, possibly under ~/.texsomethingorother/web2c. Copy it into your images/tmp directory. Lord knows what's going on here but it seems to do the business. #### LaTeX Error: File cancel.sty' not found If you see PNG conversion errors in your wiki, check the log files in images/tmp for any LaTeX errors, such as the one above. In this case, LaTeX is failing because it cannot find the file 'cancel.sty', which is missing from some texlive installations. This can be solved by installing a package named texlive-(latex-)extra, or (in Gentoo) by adding 'extra' to your USE flags when compiling texlive. Be warned that this does drag in a lot of additional packages. (cancel.sty is provided in package texlive-cancel in openSUSE and Fedora) Ubuntu 13.04 apt-get install texlive-latex-extra ### Error: Failed to parse (Cannot write to or create math temp directory) This is an error I got for an installation on: Red Hat Enterprise Linux Client release 5.6 (Tikanga) and the MediaWiki installation was done under root permission. The web server is trying to write latex related stuff into the images/tmp directory. The directory images/tmp is defined to be owned by the root user and root group. The solution: change the group of the directory to the group of the web server (in my case group=apache, user=apache): chgrp apache images/tmp and then add the write permission for the group on this directory chmod g+w images/tmp I'm not sure if it is necessary, but I have restarted httpd and reloaded the wiki page. ### Error: math_output_error This problem is related with the previous (Failed to parse). For mediawiki ver. 1.20, the solution was to set the correct permissions so that the web server can create directories below the images directory. One solution is to create the directory images/math and set the permissions: chown www-data images/math chgrp www-data images/math (Replace www-data with what your web server uses if needed) ### safe_mode If you use PHP safe_mode, you will have to patch includes/Math.php and use a wrapper script for texvc. For more details, see: http://xylofaan.ulyssis.org/patch/mediawiki/math_safe_mode/ Using safe_mode the owner of the script should be the same as the owner of the files [1]. Change the permissions to apache:apache with chown -R apache:apache <PATH_TO_MEDIAWIKI_DIRECTORY> ### Works with complicate equations but fails with simple ones My system works with a complicate equation (with fractions, integrals,...) but it fails on $\frac{dy}{dx}$ But it works when I put \,\! in the end of the line (forcing to render in .PNG) $\frac{dy}{dx}\,\!$ ### render.ml render.ml is the only file that contains commands executed by texvc. If you need to change command names or their paths, edit that file. It should be straightforward. #### Which latex, dvips, convert ... A universal fix is to change render.ml to use the env shell command in each of the let cmd_ ... = statements. To verify and see which commands are returned by the env command just try, for example, at the command prompt$ which latex.
let cmd_dvips tmpprefix = "env dvips ...
let cmd_latex tmpprefix = "env latex ...
let cmd_convert tmpprefix finalpath = "env convert ...
Then run make in the math directory again. You may need to restart Apache.
#### Permissions problem
latex doesn't have an option to specify an output directory, so it just places the output files (.log, .aux, .dvi) into the current directory. The render.ml file line
if Util.run_in_other_directory tmppath (cmd_latex tmpprefix0) != 0
handles this by calling the function run_in_other_directory defined in util.ml. Function run_in_other_directory attempts to save the current directory, change directory to the proper output (temp) directory, call latex, then change back to the previous current directory. To get the current directory, a function called Sys.getcwd is used, but if there are not sufficient permissions to read the directory (all parent directories back to the root must be readable by the user running texvc), then texvc just quits. There will be a .tex file in the temp directory, but no .dvi or other files. One way to fix this is to replace the above line of render.ml with these two lines:
Sys.chdir tmppath;
if Sys.command (cmd_latex tmpprefix) != 0
(Recompile texvc.) This will change the current directory, then run latex. Changing back to the original directory doesn't appear to be necessary.
#### Installing tetex
Rather than using a global directory, e.g. /opt/local/bin/, for installation or symlinking, your latex installation is more likely able to find its configuration files if you install everything in the teTeX directory and referencing the binaries directly.
For example, configure teTeX to install into /home/wiki/local/teTeX/ with ./configure --prefix=/home/wiki/local/teTeX/. Then, rather than symlinking them, reference them directly from render.ml, i.e.
let cmd_dvips tmpprefix = "/home/wiki/local/teTeX/bin/x86-unknown-linux-gnu/dvips ...
let cmd_latex tmpprefix = "/home/wiki/local/teTeX/bin/x86-unknown-linux-gnu/latex ...
In this way, the latex and dvips executables know their own directory and will search the immediate parents for the relevent teTeX configuration files. Without them, and without the relevant environment variables, these executables may be unable to find their configuration, and you will get a relatively generic error.
### dvipng
GhostScript, ImageMagick and dvips can be replaced by dvipng. It may be easier to configure on some systems, and would be much faster. In addition it can do transparent background (full-alpha or all-or-nothing transparency as wished). It can also report the baseline position if desired.
There is a patch for render.ml to do that, seemailarchive:wikitech-l/2004-April/009596.html The patch will make an image with a full-alpha transparent background (with dvipng >= 1.6). Remember that there are problems with IE and full-alpha transparency. To use all-or-nothing transparency with dvipng >= 1.6, use '-bg transparent' (all lowercase).
### MySQL error 1267: Illegal mix of collocations
After restoring or transferring a MySQL database:
An error message is displayed:
A database query syntax error has occurred. This may indicate a bug in the software. The last attempted database query was: (SQL query hidden) from within function "MathRenderer::_recall". MySQL returned error "1267: Illegal mix of collations (latin1_swedish_ci,IMPLICIT) and (utf8_general_ci,COERCIBLE) for operation '=' (localhost)".
Possible solution: in LocalSettings.php, change the value of \$wgDBmysql5 to false;
If this doesn't work for you, use phpMyAdmin to pull up the *wiki_math table in the wikidb, click the Structure tab, and change the collation on each column that is "latin1_swedish_ci" to "utf8_general_ci". That fixed it here. Then just do the usual things: install ocaml and latex, cd <wikidir>/math, and make to build texvc.
It seems that when upgrading older wikis up through various MySQL versions, somehow "latin1_swedish_ci" ends up getting stuffed on collation order fields at the database, table, and column levels. This is not what the built-in LaTeX "[itex]" extension wants to see. This is not fixed-up by MediaWiki's upgrade.php script.
## Selinux
On Linux systems with selinux support, such as recent versions of Fedora Core, restrictions enacted by selinux can result in puzzling manifestations. On selinux-enabled systems, it is a good idea to check for records in the selinux log files. On Fedora Core, these are found at /var/log/audit/audit.log. For testing purposes, under Fedora selinux can be disabled interactively with the command:
sudo /usr/sbin/setenforce 0
and re-enabled with the command:
sudo /usr/sbin/setenforce 1
On some systems, for example Fedora Core 7, you can obtain interesting information if you have access to the setroubleshoot browser, a tool which can be accessed from the desktop menus "System" and "Administration". Each time selinux prevents an action from being performed, for example a file access involved in the texvc machinery, it records information that can be viewed in this browser. The browser also describes how to enable the prevented access, typically by performing chcon commands on the specified file. After a sequence of such commands it may be possible to get texvc working properly without disabling selinux.
On one system where texvc was failing to work properly, the shell script was able to create files in the file system normally, but unable to write any contents to these files, where each write request generated an selinux audit log entry of the following form:
type=AVC msg=audit(1165430855.036:398755): avc: denied { write } for pid=30145
comm="httpd" name=php-eaccelerator dev=dm-0 ino=16034837 scontext=root:system_r:httpd_t
tcontext=system_u:object_r:var_t tclass=dir
MediaWiki detected this error as an empty status response from the texvc shell comamnd, as the contents of the write() call to return the status result was denied by selinux. Note that when testing texvc on the command line, the status string written by texvc to stdout does not normally contain a terminating newline, so one some shells the string will not be displayed. To verify that the status string is returning normally, one can run texvc as follows:
./math/texvc arguments > out
ls -l out # view file size
vi out # view status contents
Another option is to run texvc under strace to see that it is functioning normally.
If you are getting the error message "Error : Failed to parse (Missing texvc executable)" or the same error for texvcheck, it may be because these files don't have the necessary selinux context settings. You can check this by running:
ls -Z texvc
This will display a context like "unconfined_u:object_r:httpd_sys_content_t". That context is not sufficient to allow execution. Change the context by running:
chcon -t httpd_exec_t texvc
An alternative to trying to get texvc to work is to rewrite the Math.php render code to use PHP instead: Texvc PHP Alternative
## PaX
PaX is a security feature built into Gentoo Hardened systems designed to add extra memory protection to the kernel. Normally this is a good thing, but it plays havoc with texvc (apparently because texvc relies upon rewriting its own ELF in memory). The solution is to use the paxctl utility to disable MPROTECT on texvc and associated executables:
sudo paxctl -m math/texvc math/texvc_test math/texvc_tex
`
This should resolve the dreaded "error while loading shared libraries: cannot make segment writable for relocation: Permission denied" problem.
## Apache Chroot
Help needed on getting texvc to work with a chrooted apache.
## overleftrightarrow
The token "\overleftrightarrow" is not handled correctly by Texvc. The parser assumes that the function is part of the normal TeX distribution, whereas it is actually a part of ams-math. Therefore, if you do not have any other ams-math functions within the math tags, then it will not be rendered.
Example of overleftrightarrow on its own (known to fail)
$\overleftrightarrow{A B}$
Example of \overleftrightarrow with other ams-math functions (known to work correctly)
$\overleftrightarrow{A B} \mathit{i}$ or $\overleftrightarrow{A B} \mathit{\ }$.
|
2014-04-17 15:27:49
|
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|
https://chemistry.stackexchange.com/questions/76062/decarboxylation-mechanism-and-stability-of-%CE%B1-%CE%B2-unsaturated-and-%CE%B1-hydroxy-acids?noredirect=1
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# Decarboxylation mechanism and stability of α,β-unsaturated and α-hydroxy acids
I was wondering why α,β-unsaturated and α-hydroxy acids undergo decarboxylation. Also, I'm aware of neither the products nor mechanism. All I know is that β-keto acids and α-nitro compounds have resonance stabilized anions and have stable transition states.
But α,β-unsaturated have none of those and it isn't that electronegative as its sp2. Someone please help me out; I can't find the answer anywhere else.
• i cant find the answer anywhere else Strongly disagree: pubs.acs.org/doi/abs/10.1021/ed064p591#/doi/abs/10.1021/… – Pritt Balagopal Jun 11 '17 at 12:51
• Im sorry I cant understand it, Im not an undergraduate student can you please explain it to me? Without the oxidative cleavage or free radical hunsdicker reaction. Just how on heating aplha beta unstaurated acids undergo decarboxylation? – TheLostGuardian0 Jun 11 '17 at 12:56
• Decarboxylation mechanism involves creating a carbanion at the carbon attached to $\ce{-COOH}$ group. Does this help you decide why? – Pritt Balagopal Jun 11 '17 at 12:58
• – Pritt Balagopal Jun 11 '17 at 13:00
• @PrittBalagopal I noticed you'd linked to a J. Chem. Ed. paper in the comments (DOI: 10.1021/ed064p591). I suspect that the OP doesn't have journal access, it might be more productive to paraphrase what that paper actually says about the reaction in question – NotEvans. Jun 11 '17 at 16:23
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2019-10-24 04:12:32
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https://study.com/academy/answer/a-hummingbird-has-a-mass-of-about-1-7-g-suppose-a-hummingbird-does-0-15-j-of-work-against-gravity-so-that-it-ascends-straight-up-with-a-net-acceleration-of-1-2-m-s-squared-how-far-up-does-it-move.html
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# A hummingbird has a mass of about 1.7 g. Suppose a hummingbird does 0.15 J of work against...
## Question:
A hummingbird has a mass of about {eq}1.7 \ g {/eq}. Suppose a hummingbird does {eq}0.15 \ J {/eq} of work against gravity, so that it ascends straight up with a net acceleration of {eq}1.2 \ m / s {/eq} (squared). How far up does it move?
## Work:
Work is a form of energy transfer due to the motion of an object. Work can be defined in terms of the kinetic energy change that an object can experience, or the applied external force of motion on the object times its distance traveled. Just like with energy values, work is also expressed in joules (J).
Given:
• {eq}\displaystyle \rm m = 1.7\ g = 0.0017\ kg {/eq} is the mass of the bird
• {eq}\displaystyle \rm W = 0.15\ J {/eq} is the work done by the bird against gravity
• {eq}\displaystyle \rm a = 1.2\ m/s^2 {/eq} is the net acceleration of the bird
We can determine the distance traveled by the bird by noting that the definition of work is:
{eq}\displaystyle \rm W = Fd {/eq}
The force F here is the force done by the bird against gravity. This force, in particular, can be determined through using Newton's second law. Note that the force acts against gravity, so we actually have two forces:
{eq}\displaystyle \rm ma = F - mg {/eq}
The force is:
{eq}\displaystyle \rm F = ma + mg {/eq}
{eq}\displaystyle \rm F = m(a + g) {/eq}
We re-write our work:
{eq}\displaystyle \rm W = m(a+g)d {/eq}
We isolate our distance d:
{eq}\displaystyle \rm d = \frac{W}{m(a+g)} {/eq}
We substitute:
{eq}\displaystyle \rm d = \frac{0.15\ J}{(0.0017\ kg)(9.8\ m/s^2 + 1.2\ m/s^2)} {/eq}
We will thus get:
{eq}\displaystyle \rm \boxed{\rm d = 8.02\ m} {/eq}
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2020-06-06 09:06:38
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http://pandapower.readthedocs.io/en/v1.5.1/networks/power_system_test_cases.html
|
# Power System Test Cases¶
Note
All Power System Test Cases were converted from PYPOWER or MATPOWER case files.
## Case 4gs¶
pandapower.networks.case4gs()
This is the 4 bus example from J. J. Grainger and W. D. Stevenson, Power system analysis. McGraw-Hill, 1994. pp. 337-338. Its data origin is PYPOWER.
OUTPUT:
net - Returns the required ieee network case4gs
EXAMPLE:
import pandapower.networks as pn
net = pn.case4gs()
## Case 6ww¶
pandapower.networks.case6ww()
Calls the pickle file case6ww.p which data origin is PYPOWER. It represents the 6 bus example from pp. 104, 112, 119, 123-124, 549 from A. J. Wood and B. F. Wollenberg, Power generation, operation, and control. John Wiley & Sons, 2012..
OUTPUT:
net - Returns the required ieee network case6ww
EXAMPLE:
import pandapower.networks as pn
net = pn.case6ww()
## Case 9¶
pandapower.networks.case9()
Calls the pickle file case9.p which data origin is PYPOWER. This network was published in Anderson and Fouad’s book ‘Power System Control and Stability’ for the first time in 1980.
OUTPUT:
net - Returns the required ieee network case9
EXAMPLE:
import pandapower.networks as pn
net = pn.case9()
## Case 14¶
pandapower.networks.case14()
Calls the pickle file case14.p which data origin is PYPOWER. This network was converted from IEEE Common Data Format (ieee14cdf.txt) on 20-Sep-2004 by cdf2matp, rev. 1.11, to matpower format and finally converted to pandapower format by pandapower.converter.from_ppc. The vn_kv was adapted considering the proposed voltage levels in Washington case 14
OUTPUT:
net - Returns the required ieee network case14
EXAMPLE:
import pandapower.networks as pn
net = pn.case14()
Case 24_ieee_rts
pandapower.networks.case24_ieee_rts()
The IEEE 24-bus reliability test system was developed by the IEEE reliability subcommittee and published in 1979. Some more information about this network are given by Illinois University case 24. The data origin for this network data is PYPOWER.
OUTPUT:
net - Returns the required ieee network case24
EXAMPLE:
import pandapower.networks as pn
net = pn.case24_ieee_rts()
## Case 30¶
pandapower.networks.case30()
This function calls the pickle file case30.p which data origin is PYPOWER. Some more information about this network are given by Washington case 30 and Illinois University case 30.
OUTPUT:
net - Returns the required ieee network case30
EXAMPLE:
import pandapower.networks as pn
net = pn.case30()
## Case 33bw¶
pandapower.networks.case33bw()
Calls the pickle file case33bw.p which data is provided by MATPOWER. The data origin is the paper M. Baran, F. Wu, Network reconfiguration in distribution systems for loss reduction and load balancing IEEE Transactions on Power Delivery, 1989.
OUTPUT:
net - Returns the required ieee network case33bw
EXAMPLE:
import pandapower.networks as pn
net = pn.case33bw()
## Case 39¶
pandapower.networks.case39()
Calls the pickle file case39.p which data origin is PYPOWER. This network was published the first time in G. Bills et al., On-line stability analysis study, RP 90-1, E. P. R. I. North American Rockwell Corporation, Edison Electric Institute, Ed. IEEE Press, Oct. 1970,. Some more information about this network are given by Illinois University case 39. Because the Pypower data origin proposes vn_kv=345 for all nodes the transformers connect node of the same voltage level.
OUTPUT:
net - Returns the required ieee network case39
EXAMPLE:
import pandapower.networks as pn
net = pn.case39()
## Case 57¶
pandapower.networks.case57(vn_kv_area1=115, vn_kv_area2=500, vn_kv_area3=138, vn_kv_area4=345, vn_kv_area5=230, vn_kv_area6=161)
This function provides the ieee case57 network with the data origin PYPOWER case 57. Some more information about this network are given by Illinois University case 57. Because the Pypower data origin proposes no vn_kv some assumption must be made. There are six areas with coinciding voltage level. These are:
• area 1 with coinciding voltage level comprises node 1-17
• area 2 with coinciding voltage level comprises node 18-20
• area 3 with coinciding voltage level comprises node 21-24 + 34-40 + 44-51
• area 4 with coinciding voltage level comprises node 25 + 30-33
• area 5 with coinciding voltage level comprises node 41-43 + 56-57
• area 6 with coinciding voltage level comprises node 52-55 + 26-29
OUTPUT:
net - Returns the required ieee network case57
EXAMPLE:
import pandapower.networks as pn
net = pn.case57()
## Case 89pegase¶
pandapower.networks.case89pegase()
Calls the pickle file case89pegase.p which data is provided by MATPOWER. The data origin are the paper C. Josz, S. Fliscounakis, J. Maenght, P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, 2016 and S. Fliscounakis, P. Panciatici, F. Capitanescu, and L. Wehenkel, Contingency ranking with respect to overloads in very large power systems taking into account uncertainty, preventive, and corrective actions, IEEE Transactions on Power Systems, vol. 28, no. 4, pp. 4909-4917, Nov 2013..
OUTPUT:
net - Returns the required ieee network case89pegase
EXAMPLE:
import pandapower.networks as pn
net = pn.case89pegase()
## Case 118¶
pandapower.networks.case118()
OUTPUT:
net - Returns the required ieee network case118
EXAMPLE:
import pandapower.networks as pn
net = pn.case118()
## Case 145¶
pandapower.networks.case145()
Calls the pickle file case145.p which data origin is MATPOWER. This data is converted by MATPOWER 5.1 using CDF2MPC on 18-May-2016 from ‘dd50cdf.txt’.
OUTPUT:
net - Returns the required ieee network case145
EXAMPLE:
import pandapower.networks as pn
net = pn.case145()
## Case 300¶
pandapower.networks.case300()
OUTPUT:
net - Returns the required ieee network case300
EXAMPLE:
import pandapower.networks as pn
net = pn.case300()
## Case 1354pegase¶
pandapower.networks.case1354pegase()
This grid represents a part of the European high voltage transmission network. The data is provided by MATPOWER. The data origin are the paper C. Josz, S. Fliscounakis, J. Maenght, P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, 2016 and S. Fliscounakis, P. Panciatici, F. Capitanescu, and L. Wehenkel, Contingency ranking with respect to overloads in very large power systems taking into account uncertainty, preventive, and corrective actions, IEEE Transactions on Power Systems, vol. 28, no. 4, pp. 4909-4917, Nov 2013..
OUTPUT:
net - Returns the required ieee network case1354pegase
EXAMPLE:
import pandapower.networks as pn
net = pn.case1354pegase()
## Case 1888rte¶
pandapower.networks.case1888rte(ref_bus_idx=1246)
This case accurately represents the size and complexity of French very high voltage and high voltage transmission network. The data is provided by MATPOWER. The data origin is the paper C. Josz, S. Fliscounakis, J. Maenght, P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, 2016.
OPTIONAL:
ref_bus_idx - Since the MATPOWER case provides a reference bus without connected generator, because a distributed slack is assumed, to convert the data to pandapower, another bus has been assumed as reference bus. Via ‘ref_bus_idx’ the User can choose a reference bus, which should have a generator connected to. Please be aware that by changing the reference bus to another bus than the proposed default value, maybe a powerflow does not converge anymore!
OUTPUT:
net - Returns the required ieee network case1888rte
EXAMPLE:
import pandapower.networks as pn
net = pn.case1888rte()
## Case 2848rte¶
pandapower.networks.case2848rte(ref_bus_idx=271)
This case accurately represents the size and complexity of French very high voltage and high voltage transmission network. The data is provided by MATPOWER. The data origin is the paper C. Josz, S. Fliscounakis, J. Maenght, P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, 2016.
OPTIONAL:
ref_bus_idx - Since the MATPOWER case provides a reference bus without connected generator, because a distributed slack is assumed, to convert the data to pandapower, another bus has been assumed as reference bus. Via ‘ref_bus_idx’ the User can choose a reference bus, which should have a generator connected to. Please be aware that by changing the reference bus to another bus than the proposed default value, maybe a powerflow does not converge anymore!
OUTPUT:
net - Returns the required ieee network case2848rte
EXAMPLE:
import pandapower.networks as pn
net = pn.case2848rte()
## Case 2869pegase¶
pandapower.networks.case2869pegase()
This grid represents a part of the European high voltage transmission network. The data is provided by MATPOWER. The data origin i the paper C. Josz, S. Fliscounakis, J. Maenght, P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, 2016 and S. Fliscounakis, P. Panciatici, F. Capitanescu, and L. Wehenkel, Contingency ranking with respect to overloads in very large power systems taking into account uncertainty, preventive, and corrective actions, IEEE Transactions on Power Systems, vol. 28, no. 4, pp. 4909-4917, Nov 2013..
OUTPUT:
net - Returns the required ieee network case2869pegase
EXAMPLE:
import pandapower.networks as pn
net = pn.case2869pegase()
## Case 3120sp¶
pandapower.networks.case3120sp()
This case represents the Polish 400, 220 and 110 kV networks during summer 2008 morning peak conditions. The data was provided by Roman Korab <roman.korab@polsl.pl> and to pandapower converted from MATPOWER.
OUTPUT:
net - Returns the required ieee network case3120sp
EXAMPLE:
import pandapower.networks as pn
net = pn.case3120sp()
## Case 6470rte¶
pandapower.networks.case6470rte(ref_bus_idx=5988)
This case accurately represents the size and complexity of French very high voltage and high voltage transmission network. The data is provided by MATPOWER. The data origin is the paper C. Josz, S. Fliscounakis, J. Maenght, P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, 2016.
OPTIONAL:
ref_bus_idx - Since the MATPOWER case provides a reference bus without connected generator, because a distributed slack is assumed, to convert the data to pandapower, another bus has been assumed as reference bus. Via ‘ref_bus_idx’ the User can choose a reference bus, which should have a generator connected to. Please be aware that by changing the reference bus to another bus than the proposed default value, maybe a powerflow does not converge anymore!
OUTPUT:
net - Returns the required ieee network case6470rte
EXAMPLE:
import pandapower.networks as pn
net = pn.case6470rte()
## Case 6495rte¶
pandapower.networks.case6495rte(ref_bus_idx=None)
This case accurately represents the size and complexity of French very high voltage and high voltage transmission network. The data is provided by MATPOWER. The data origin is the paper C. Josz, S. Fliscounakis, J. Maenght, P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, 2016.
OPTIONAL:
ref_bus_idx - Since the MATPOWER case provides a reference bus without connected generator, because a distributed slack is assumed, to convert the data to pandapower, another buses (6077, 6161, 6305, 6306, 6307, 6308) has been assumed as reference bus. Via ‘ref_bus_idx’ the User can choose a reference bus, which should have a generator connected to. Please be aware that by changing the reference bus to another bus than the proposed default value, maybe a powerflow does not converge anymore!
OUTPUT:
net - Returns the required ieee network case6495rte
EXAMPLE:
import pandapower.networks as pn
net = pn.case6495rte()
## Case 6515rte¶
pandapower.networks.case6515rte(ref_bus_idx=6171)
This case accurately represents the size and complexity of French very high voltage and high voltage transmission network. The data is provided by MATPOWER. The data origin is the paper C. Josz, S. Fliscounakis, J. Maenght, P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, 2016.
OPTIONAL:
ref_bus_idx - Since the MATPOWER case provides a reference bus without connected generator, because a distributed slack is assumed, to convert the data to pandapower, another bus has been assumed as reference bus. Via ‘ref_bus_idx’ the User can choose a reference bus, which should have a generator connected to. Please be aware that by changing the reference bus to another bus than the proposed default value, maybe a powerflow does not converge anymore!
OUTPUT:
net - Returns the required ieee network case6515rte
EXAMPLE:
import pandapower.networks as pn
net = pn.case6515rte()
## Case 9241pegase¶
pandapower.networks.case9241pegase()
This grid represents a part of the European high voltage transmission network. The data is provided by MATPOWER. The data origin are the paper C. Josz, S. Fliscounakis, J. Maenght, P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, 2016 and S. Fliscounakis, P. Panciatici, F. Capitanescu, and L. Wehenkel, Contingency ranking with respect to overloads in very large power systems taking into account uncertainty, preventive, and corrective actions, IEEE Transactions on Power Systems, vol. 28, no. 4, pp. 4909-4917, Nov 2013..
OUTPUT:
net - Returns the required ieee network case9241pegase
EXAMPLE:
import pandapower.networks as pn
net = pn.case9241pegase()
## Case GB network¶
pandapower.networks.GBnetwork()
Calls the pickle file GBnetwork.p which data is provided by W. A. Bukhsh, Ken McKinnon, Network data of real transmission networks, April 2013. This data represents detailed model of electricity transmission network of Great Britian (GB). It consists of 2224 nodes, 3207 branches and 394 generators. This data is obtained from publically available data on National grid website. The data was originally pointing out by Manolis Belivanis, University of Strathclyde.
OUTPUT:
net - Returns the required ieee network GBreducednetwork
EXAMPLE:
import pandapower.networks as pn
net = pn.GBnetwork()
## Case GB reduced network¶
pandapower.networks.GBreducednetwork()
Calls the pickle file GBreducednetwork.p which data is provided by W. A. Bukhsh, Ken McKinnon, Network data of real transmission networks, April 2013. This data is a representative model of electricity transmission network in Great Britain (GB). It was originally developed at the University of Strathclyde in 2010.
OUTPUT:
net - Returns the required ieee network GBreducednetwork
EXAMPLE:
import pandapower.networks as pn
net = pn.GBreducednetwork()
## Case iceland¶
pandapower.networks.iceland()
Calls the pickle file iceland.p which data is provided by W. A. Bukhsh, Ken McKinnon, Network data of real transmission networks, April 2013. This data represents electricity transmission network of Iceland. It consists of 118 nodes, 206 branches and 35 generators. It was originally developed in PSAT format by Patrick McNabb, Durham University in January 2011.
OUTPUT:
net - Returns the required ieee network iceland
EXAMPLE:
import pandapower.networks as pn
net = pn.iceland()
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2018-07-22 02:45:02
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http://stats.stackexchange.com/questions/29546/p-value-vs-confidence-interval-obtained-in-bootstrapping
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# p-value vs. confidence interval obtained in Bootstrapping
I ran a simple randomized experiment with 1 control and 1 experimental condition (final N = 80). The dependent variable (frequency of a shown behavior) is clearly not normally distributed so I thought about bootstrapping my analysis (an independent t-test).
The t-test without bootstrapping resulted in a significant effect between the conditions (p < .05). Using SPSS, the p-value based on bootstrapping (5000 resamples) is only marginally significant (p < .10). However, the 95% confidence interval does not include zero.
I just apply statistical methods and sometimes I don't know what is actually right (unfortunately!). But that's why I ask this question. When I tried to learn how Bootstrapping works, I thought that one has to look at the confidence intervals to detect whether an effect is not zero. In my example above, the 95% CI does not accompany with the bootstrapped p-value. So I don't know whether I should report the bootstrapped CI and/or the bootstrapped p-value and/or the typical unbootstrapped p-value.
What would you say?
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I am not an SPSS expert, but to me it looks like it will be difficult to help you if people do not know what is your data, how you bootstrapped it and what score you measured in the end. – gui11aume May 31 '12 at 9:46
I am not a real Bootstrap expert, but I can tell you about the two main things:
1. Bootstrap confidence intervals are usually more robust and accurate then the ones estimated without bootstrap.
2. If you estimate the parameter with bootstrap, your confidence interval (CI) usually evaluated in a different way then in a regular t-test. For example, in a regular case CI is $[ \hat{\theta} - \hat{q}_{1-\alpha/2}, \hat{\theta} + \hat{q}_{\alpha/2} ]$ (here $\hat{\theta}$ is an estimate of the parameter, $\hat{q}_{\alpha}$ is an $\alpha$-quantile). But for bootstrap it is $[ \hat{\theta} - \hat{q}_{1-\alpha/2}, \hat{\theta} - \hat{q}_{\alpha/2} ]$ (minus sign in both cases).
From that all I would suggest you to recheck whether with this formulas bootstrap CI accompany with the p-value. And if you will find that it's ok now, report bootstrapped results. If no, it is better to ask SPSS experts about how bootstrap works there.
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You have many choices for bootstrap confidence intervals. All bootstrap confidence intervals are approximate and do not always do well in small samples (usually 80 is not considered small). also if you read Hall and Wilson's paper you will find that testing hypotheses assuming the bootstrap distribution under the null hypothesis works better than inverting confidence intervals. It is an issue about how to center the pivotal quantity in the test statistics. Schenker in 1985 showed that bootstrap methods such as Efron's percentile method and even the BC method severely under cover the true parameter for certain chi square populations when the sample size is not very large. Chernick and LaBudde in 2010 American Journal of Mathematical and Management Science showed that in small samples there can even be problems with BCa and bootstrap t for highly skewed distributions such as the lognormal. So based on the literature including my own research I suggest doing the hypothesis test with the centering approach recommended by Hall and Wilson and base your conclusions on that p-value. You can find detailed coverage of this in my recent book "An Introduction to the Bootstrap with Applications to R" published by Wiley in 2011.
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Since this isn't an academic paper, a link to referenced articles is better than a citation IMO. – Michael McGowan May 31 '12 at 15:29
Yes but it also takes very little effort to use the citation on Google to find any link I might give and others. Some of the links might have the paper available to read either for free or for some small fee. – Michael Chernick May 31 '12 at 15:41
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2013-05-18 06:42:53
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http://www.codeproject.com/Articles/2145/Dependency-Grapher-for-C-Projects?fid=3688&df=90&mpp=10&sort=Position&spc=None&tid=766493
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12,507,674 members (55,826 online)
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# Dependency-Grapher for C++-Projects
, 8 Jul 2002
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An add-in written in VB.NET to generate an inheritance and/or dependency graph of a c++-project. Uses the graphviz library from AT&T.
<!-- Article image -->
## Description
ClassDep is an add-in which generates a JPEG or JPG image showing an inheritance and/or a dependency graph of a C++ project in visual studio. is uses the graphviz tools from http://www.research.att.com/sw/tools/graphviz/. The picture above shows the generated dependency graph of one of my projects.
## Installation
Just double-click on the msi file and follow the installation instructions. All files from the graphviz library are included in the msi file.
## Usage
to use the addin simply click on the ClassDep-Entry in the Tool-Menu of Visual Studio .NET. It only works for C++ projects (C# and VB are not supported). The resulting picture files are stored in the corresponding project folder with the name(s) projectdep.jpg and/or projectdep.png. Please note that the picture files may become really huge for big projects!
## Implementation
for generating inheritance/dependency graphs it is usually necessary to parse the source code. but you sure have already noticed that visual studio does that in the "class-view"-window - it shows the base classes and the members of all project classes. So I wondered if and how I could use this built-in functionality of visual studio for my needs. the DTE-object was the perfect solution:
Dim applicationObject As EnvDTE.DTE
Dim project As Project
For Each project In applicationObject.ActiveSolutionProjects()
'...
'read out all c++-related object in the current project
BuildObjectList(project.CodeModel.CodeElements, 0)
For Each cl In project.CodeModel.CodeElements
If (cl.Kind = vsCMElement.vsCMElementClass) Then
'cl is a class
ScanBases(cl, 0) 'scan all base classes/structs
depfile.WriteLine(";")
If (ob.dependency.Checked) Then
ScanDependencies(cl) 'also scan all dependencies of the class
End If
End If
Next
'...
I started first with a macro and then decided to switch to an add-in because of the easier installation. That's the reason why this add-in is written in VB.
one problem of an addin is that I don't know a way to get the path of where the addin-dll is installed. that is also the path where the graphviz files are installed and I need to know that to use these files. the only way I know of is by using the registry. So the installation msi writes also a registry entry with the installation path:
Dim dotdir As String
dotdir = Registry.LocalMachine.OpenSubKey( _
False).GetValue("instpath", " ")
and last the call to the graphviz tools:
If ob.outjpeg.Checked Then
'call the graphviz tool with required params to generate the jpeg
Shell(dotdir + "\dot.exe -Tjpg """ + dir + "dep.txt"" -o """ + dir +_
project.Name + "dep.jpg""", AppWinStyle.MinimizedFocus, True)
End If
If ob.outpng.Checked Then
Shell(dotdir + "\dot.exe -Tpng """ + dir + "dep.txt"" -o """ + dir +_
project.Name + "dep.png""", AppWinStyle.MinimizedFocus, True)
End If
## Conclusion
There are a lot of improvements possible like a better ordering of the dependency graph and the like. Some of you might find the colors awful - feel free to change that :-)
I also included the graphviz files inside the msi-installer. As far as I understand the license of the graphviz this is allowed - mail me if I'm wrong.
If someone knows how to change that ugly smiley-icon of the menu-entry please let me know!
## History
July 15 2002 - fixed uncaught exception bug found by Brian D Pearson
A list of licenses authors might use can be found here
## Share
Software Developer Switzerland
---
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2016-09-29 00:37:45
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https://www.tutorialspoint.com/count-pairs-from-two-arrays-whose-modulo-operation-yields-k-in-cplusplus
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# Count pairs from two arrays whose modulo operation yields K in C++
We are given two arrays containing positive numbers and a value K. The goal is to find unique pairs of elements of arrays such that pairs of type (A,B) has A%B=K or B%A=K and A belongs to the first array and B belongs to the second array.
Let us understand with examples
Input − arr_1[] = {1,2,5,3,4}; arr_2[] = {7,1,3}; k=2
Output − Count of pairs from two arrays whose modulo operation yields K are − 2
Explanation − The pairs are (5,7) - (arr_1[2],arr_2[1]) 7%5=2 and (5,3) - (arr_1[2],arr_2[2]) 5%3=2
Input − arr_1[] = {2,5}; arr_2[] = {3,7}; k=1
Output − Count of pairs from two arrays whose modulo operation yields K are − 2
Explanation − The pairs are (2,3) - (arr_1[0],arr_2[0]) 3%2=1 and (2,7) - (arr_1[0],arr_2[1]) 7%2=1
## Approach used in the below program is as follows
In this approach we will traverse both arrays using for loop. Insert pairs to set<pair<int, int> > se in which A%B=k or B%A=k, where A belongs to arr_1 and B belongs to arr_2. At the end size of set se is the number of unique pairs from two arrays whose modulo operation yields k.
• Take integer arrays arr_1[] and arr_2[] with positive elements and lengths as size_arr_1 and size_arr_2.
• Take integers k.
• Function modulo_pairs(int arr_1[], int arr_2[], int size_arr_1, int size_arr_2, int k) takes both arrays and their lengths and returns the pairs such that the modulo operation of elements of both arrays yields k.
• Take the initial value of count as 0.
• Take set<pair<int, int> > se; of pairs <int,int>.
• Start traversing arr_1[] from i=0 to i<size_arr_1 and arr_2[] from j=0 to j<size_arr_2.
• For each pair arr_1[i], arr_2[j], check if arr_1[i]>arr_2[j]. If yes check if arr_1[i]%arr_2[j]==k. If true then make a pair of arr_1[i] and arr_2[j] and insert to set se.
• Else check if arr_2[j]%arr_1[i]==k. If true then make a pair of arr_1[i] and arr_2[j] and insert to set se.
• Calculate count as se.size(). For count of unique pairs.
• Return count as result.
## Example
Live Demo
#include <bits/stdc++.h>
using namespace std;
int modulo_pairs(int arr_1[], int arr_2[], int size_arr_1, int size_arr_2, int k){
int count = 0;
set<pair<int, int> > se;
for (int i = 0; i < size_arr_2; i++){
for (int j = 0; j < size_arr_1; j++){
if (arr_1[i] > arr_2[j]){
if (arr_1[i] % arr_2[j] == k){
se.insert(make_pair(arr_1[i], arr_2[j]));
}
}
else{
if (arr_2[j] % arr_1[i] == k){
se.insert(make_pair(arr_2[j], arr_1[i]));
}
}
}
}
count = se.size();
return count;
}
int main(){
int arr_1[] = { 2, 7, 1, 9 };
int arr_2[] = { 4, 10, 3, 10 };
int size_arr_1 = sizeof(arr_1) / sizeof(arr_1[0]);
int size_arr_2 = sizeof(arr_2) / sizeof(arr_2[0]);
int k = 3;
cout<<"Count of pairs from two arrays whose modulo operation yields K are:"<<modulo_pairs(arr_1, arr_2, size_arr_1, size_arr_2, k);
return 0;
}
## Output
If we run the above code it will generate the following output −
Count of pairs from two arrays whose modulo operation yields K are: 2
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2023-02-01 15:00:07
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https://electronics.stackexchange.com/questions/138604/parallel-port-as-ttl-serial
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# Parallel port as TTL serial
Is it possible to use a parallel port (a real one, not an USB converter) as a TTL serial port equivalent, for a maximum speed of 115200 baud ?
I'd like to talk to a router's serial port but I don't have any TTL level converter, and buying one is not an option (I can't afford to "waste" 20 bucks on a stupid "hey let's reverse engineer this router!" idea).
• @WoutervanOoijen I was talking about buying one already made, which is about 20 bucks with shipping. Of course it's cheaper if you buy the parts and assemble it yourself but I prefer to avoid that. – user40669 Nov 14 '14 at 20:30
• @WoutervanOoijen but since you say it's impossible, you may as well post that as an answer. Thanks. – user40669 Nov 14 '14 at 20:31
• It probably is possible to bit-bang serial at fairly high baud rates on a true localbus parallel port, if you write your own bare-metal program dedicated exclusively to that goal. It is probably not possible under a general purpose desktop O/S. – Chris Stratton Nov 14 '14 at 20:43
• While a converter could well prove to be as simple as a pair of transistorized (or IC) inverters. – Chris Stratton Nov 14 '14 at 20:43
• As @ChrisStratton says, a couple NPN transistors, four resistors and a diode would 99.9% likely work (needs a 5V supply from somewhere). – Spehro Pefhany Nov 14 '14 at 20:57
So although it would be possible, it's really not worth the huge amount of effort, when all you really need is a little USB dongle that you can pick up for $3 on eBay. Using the parallel port as a serial port: not without adding parallel-to-serial conversion hardware. A serial-port-to/from-TTL converter can be as simple as a max232 chip and a few 1uF capacitors. If that costs you 20 bucks you are visiting the wrong shops. Did you ever check www.dx.com? Free shipping... http://www.dx.com/p/usb-to-ttl-cp2102-serial-module-red-309988 http://www.dx.com/p/3v-5v-serial-port-rs232-to-ttl-converter-module-340324 Note: As an USB-to-serial converter the CP2102 (and everything else that isn't an FT chip) doesn't have the best reputation, but is is cheap... • I ordered some small prototype boards from dx -- maybe$20 out of a much larger order. For some reason, just those got hung up in customs, and took about 4 months to reach me. dx was communicative, but it was a bummer, and I had to order much more expensive boards in a rush to equip a summer course I was teaching. – Scott Seidman Nov 14 '14 at 20:40
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2021-04-14 10:33:30
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http://www.math.snu.ac.kr/board/index.php?mid=colloquia&sort_index=room&order_type=desc&page=8&l=en&document_srl=813569
|
※ 줌(zoom) 병행
URL: https://snu-ac-kr.zoom.us/j/86156396440
회의 ID: 86156396440
The thirteen books "Elements" were written or collected by Euclid of Alexandria about 300 BCE.
Many think that "Elements" is the most important example of deductive mathematics.
In fact, the Common Notions and the Postulates of Elements are not just arbitrary axioms.
They should be regarded as marvelous pearls in the ocean of geometry.
Discovering and proving theorems are the Arts of Mathematics.
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2023-01-30 12:03:02
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https://charisontreetopspa.com/narrangullen/example-of-using-fourier-transformation.php
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# Transformation fourier of example using
Home » Narrangullen » Example of using fourier transformation
## 6.7.3. Guidelines for using the Fourier Transformation Feature
Fourier Transform an overview ScienceDirect Topics. Example •Using Lagrange’s formula, –Using Fast Fourier Transform (FFT) and its inverse, we can do evaluation and interpolation in time О(рќ‘›logрќ‘›)., For example: W kn W (k N)n W k (n • Using the Fourier series representation we have Discrete • The Fast Fourier Transform does not refer to a new or different.
### Fourier transform Simple English Wikipedia the free
fft Aforge fourier transform using C# - Stack Overflow. Understanding Fast Fourier Transform from scratch — to solve Polynomial For example, 𝐴 We use the Inverse Fourier Transform to get the coefficient, The Fourier Transform As we have use complex exponentials because they lead to less writing Example 2 Suppose that a signal consists of a single rectangular.
The basics and examples for continuous and discrete Fourier transforms for engineering. The Discrete Time Fourier Transform How to Use the Discrete Fourier Transform. can you help me with this question find $\sin$ Fourier transform of $\frac{\sin{x}}{x}$
–The convolution theorem says that the Fourier transform of the convolution of two functions is equal to the product of their individual Fourier transforms Lecture 7 -The Discrete Fourier Transform example Let the continuous troducing discontinuities when using a finite number of points from the sequence
The basics and examples for continuous and discrete Fourier transforms for engineering. The Discrete Time Fourier Transform How to Use the Discrete Fourier Transform. Example: the Fourier Transform of a Gaussian, exp Some examples and theorems the Fourier Transform of a rectangle function: rect(t) 1/2 1/2 1/2 1/2 1
The Fourier Transform 1.1 Fourier transforms as integrals Example 1 Find the Fourier transform of f(t) = exp(j tj) and hence using inversion, frequency and then using the discrete Fourier transforms rapidly with the Fast Fourier Transform Fast Fourier Transform FFT Examples using the function:
Example of a Fourier Transform we don’t need the continuous Fourier transform. Instead we use the discrete Fourier transform, The Fast Fourier Transform Using Fourier Transforms For example, to transform an 8-by-8 real image to the frequency domain, first each row is transformed and packed as shown in Figure 2-4.
Fourier Transforms Fourier transform are use in many areas of geophysics such as image processing, time series 1.3 Examples of Fourier Transforms Home / Signals and Systems / Fourier Transform and Inverse Fourier Transform with Examples and Solutions. Fourier Transform and Inverse Fourier Transform using
In this article I’ll show you how to use Fast Fourier Transform in Digital Signal Processing and how to apply forward and inverse FFT on Examples using dft Examples of the Fourier Transform. Those are examples of the Fourier Transform. Examples of Fourier Transforms (Continued) Transforms of singularity functions.
Introduction to Fourier Transforms was periodic with period T by using the values of x(t) The Fourier transform of a sine or cosine at a frequency f The Fourier transform of f is therefore a function of the new variable . This function, evaluated at , is . Example 7 The Fourier transform of f given by
can you help me with this question find $\sin$ Fourier transform of $\frac{\sin{x}}{x}$ Examples showing how to use the basic . using System; using System example in C# showing how to use the basic Fast Fourier Transform
Guidelines for using the Fourier Transformation Feature. For example, the Fourier Transformation method can handle a once-per-revolution disturbance on a blade Introduction to Fourier Transforms was periodic with period T by using the values of x(t) The Fourier transform of a sine or cosine at a frequency f
An example of this is a filter which blocks high frequencies. The Fast Fourier Transform is a method computers use to quickly calculate a Fourier transform. Fast Fourier transform with examples in MATLAB Parsiad Azimzadeh 3 Fast Fourier transform Image compression is one possible use of the DFT.
This section deals with the task of creating time-domain signals out of individual sinewave components in the frequency domain. First, download this Fourier example Example •Using Lagrange’s formula, –Using Fast Fourier Transform (FFT) and its inverse, we can do evaluation and interpolation in time О(рќ‘›logрќ‘›).
In this section we define the Fourier Series, If you go back and take a look at Example 1 in the Fourier For a Fourier series we are actually using the A Tutorial on Fourier Analysis Fourier Transform as sum of sines and A Tutorial on Fourier Analysis Example A Tutorial on Fourier Analysis Filtering using DFT
Home / Signals and Systems / Fourier Transform and Inverse Fourier Transform with Examples and Solutions. Fourier Transform and Inverse Fourier Transform using Let me leave a link to this awesome Fourier transformation fourier transform with an example on time domain the Fourier series using
Examples of the Fourier Transform. Those are examples of the Fourier Transform. Examples of Fourier Transforms (Continued) Transforms of singularity functions. Examples of the Fourier Transform. Those are examples of the Fourier Transform. Examples of Fourier Transforms (Continued) Transforms of singularity functions.
The basics and examples for continuous and discrete Fourier transforms for engineering. The Discrete Time Fourier Transform How to Use the Discrete Fourier Transform. Aforge: fourier transform using C#. If for some reason you need to do a fourier transformation without see for example dsp.stackexchange.com/a/745
Fast Fourier transform with examples in MATLAB Parsiad Azimzadeh 3 Fast Fourier transform Image compression is one possible use of the DFT. Examples of the Fourier Transform. Those are examples of the Fourier Transform. Examples of Fourier Transforms (Continued) Transforms of singularity functions.
### How to Implement the Fourier Transformation from Computed
Using Fourier transform to detect large orders Part 1. The Fast Fourier Transform Using the DFT, the Fourier transform of any The block diagram in Figure 23 shows an example that converts the result of the power, To find the Fourier Transform of images using OpenCV; ( Some links are added to Additional Resources which explains frequency transform intuitively with examples)..
### Dory Spreadsheet A ftr) Fourier Analysis Using
An Intuitive Explanation of Fourier Theory. Lecture 7 -The Discrete Fourier Transform example Let the continuous troducing discontinuities when using a finite number of points from the sequence • There is a great advantage using an Fourier Image 1 0 [0 0] a 11 a 12 [a 21 a 22] Fourier Transform 2D - Example x y f(x,y) 1/2 1/2 1.
• Fourier transform Simple English Wikipedia the free
• Fourier Transforms MATLAB & Simulink - MathWorks Australia
• For example, when somebody plays laplace transform is a frequency domain representation of a continuous time signal.. whereas we use fourier transform can be Aforge: fourier transform using C#. If for some reason you need to do a fourier transformation without see for example dsp.stackexchange.com/a/745
frequency and then using the discrete Fourier transforms rapidly with the Fast Fourier Transform Fast Fourier Transform FFT Examples using the function: Home / Signals and Systems / Fourier Transform and Inverse Fourier Transform with Examples and Solutions. Fourier Transform and Inverse Fourier Transform using
Fourier Series as T → ∞ 6: Fourier Transform • Fourier Series as T → ∞ • Fourier Transform • Fourier Transform Examples • Dirac Delta Function The basics and examples for continuous and discrete Fourier transforms for engineering. The Discrete Time Fourier Transform How to Use the Discrete Fourier Transform.
Examples showing how to use the basic . using System; using System example in C# showing how to use the basic Fast Fourier Transform Solve 2tu x+ 3u t= 0; u(x;0) = f(x) using Fourier Transforms. Take the Fourier Transform of both equations. The initial condition gives bu(w;0) = fb(w)
Aforge: fourier transform using C#. If for some reason you need to do a fourier transformation without see for example dsp.stackexchange.com/a/745 For example: W kn W (k N)n W k (n • Using the Fourier series representation we have Discrete • The Fast Fourier Transform does not refer to a new or different
Using Fourier Transforms For example, to transform an 8-by-8 real image to the frequency domain, first each row is transformed and packed as shown in Figure 2-4. Fourier Transforms. For example, create a new signal Using the Fourier transform formula directly to compute each of the elements of requires on the order of
Fast Fourier transform with examples in MATLAB Parsiad Azimzadeh 3 Fast Fourier transform Image compression is one possible use of the DFT. In this section we define the Fourier Series, If you go back and take a look at Example 1 in the Fourier For a Fourier series we are actually using the
Discrete Fourier Transform OpenCV examples tutorial code Learn OpenCV by Examples OpenCV simplified for beginners by the use of examples. The Fourier transform is a mathematical technique For example, the Fourier expansion One entry that deserves special notice because of its common use in RF
Fourier Series as T → ∞ 6: Fourier Transform • Fourier Series as T → ∞ • Fourier Transform • Fourier Transform Examples • Dirac Delta Function Home / Signals and Systems / Fourier Transform and Inverse Fourier Transform with Examples and Solutions. Fourier Transform and Inverse Fourier Transform using
Using FFT/IFT In ImageMagick Implementation Notes ImageMagick makes use of the FFTW, Discrete Fourier Transform Library which requires images to be converted to and In this article I’ll show you how to use Fast Fourier Transform in Digital Signal Processing and how to apply forward and inverse FFT on Examples using dft
Introduction to Fourier Transforms was periodic with period T by using the values of x(t) The Fourier transform of a sine or cosine at a frequency f The Fourier transform is a mathematical technique For example, the Fourier expansion One entry that deserves special notice because of its common use in RF
FOURIER SERIES AND INTEGRALS So we use this: I will go immediately to the most important example of a Fourier sine series. S(x) In this article I’ll show you how to use Fast Fourier Transform in Digital Signal Processing and how to apply forward and inverse FFT on Examples using dft
Let me leave a link to this awesome Fourier transformation fourier transform with an example on time domain the Fourier series using • There is a great advantage using an Fourier Image 1 0 [0 0] a 11 a 12 [a 21 a 22] Fourier Transform 2D - Example x y f(x,y) 1/2 1/2 1
Using the inverse Fourier transformation, this is a good example of a visualization action that would take a lot more time in other software or if you used a I would like to validate the following code of a Fourier transform using Matlab's fft, N-points Transform. Many of the examples online use an explicit N-points
can you help me with this question find $\sin$ Fourier transform of $\frac{\sin{x}}{x}$ Using Fourier transform to detect large orders: Part 1 Therefore, for example, if we reveal that a TWAP buy-scheme is being implemented at the moment,
So for example a transform on 1024 points using the DFT takes about 100 times longer than using the (Fast Fourier Transform) Fast Fourier Transforms Walker, For example: W kn W (k N)n W k (n • Using the Fourier series representation we have Discrete • The Fast Fourier Transform does not refer to a new or different
The Fourier transform of f is therefore a function of the new variable . This function, evaluated at , is . Example 7 The Fourier transform of f given by A Tutorial on Fourier Analysis Fourier Transform as sum of sines and A Tutorial on Fourier Analysis Example A Tutorial on Fourier Analysis Filtering using DFT
Shopify Now Offers Ecommerce Policy Templates You’ll also see this policy referred to as “terms and conditions”, What Should I Name My Online Store? Example terms and conditions for online store Yea Online Costume Store - Costume Direct. The website costumedirect.com.au and shop.costumedirect.com.au is owned and operated as an online costume store by All Costumes
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2021-04-11 11:53:42
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https://www.studyadda.com/sample-papers/mathematics-sample-paper-3_q12/334/308177
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• # question_answer Find the ratio of the following: (a) 30 minutes to $1.5$hours (b) 40 cm to $1.5\,m$ (c) 55 paise to Rs. 1 (d) 500 ml to 2 litres
(a) 30 minutes to 1.5 hours = 30 min.: 90 min. {$\because$1 hour = 60 minutes, 1.5 hours $=1.5\times 60=90\text{ }min.$} $=30:90$ $=1:3$ (b) 40 cm to 1.5m $=40\text{ }cm.:1.5\times 100\text{ }cm.$ {$\because$$1\text{ }m=100\text{ }cm.,1.5\text{ }m=1.5\times 100\text{ }cm$} $=40\text{ }cm.:150\text{ }cm.$ $=40:150=\frac{40}{150}=\frac{4}{15}$ $=4:15$ (c) 55 paise to Rs. 1 = 55 paise : 100 paise {Rs. 1 = 100 paises} $=55:100=\frac{55}{100}=\frac{11}{20}$ $=11:20$ (d) 500 ml to 2 litre = 500 ml.: 2000 ml. {$\because$1 litre =1000 ml., $=500:2000=\frac{500}{2000}=\frac{1}{4}$ $\therefore$ {2 litre = 2000 ml.} $=1:4$
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2020-09-30 23:18:13
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http://clay6.com/qa/40831/write-the-following-as-intervals-iv-
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Home >> CBSE XI >> Math >> Sets
Write the following as intervals :(iv) $\{x : x\in R,3 \leq x\leq 4\}$
$\begin{array}{1 1}(A)\;[3,4]&(B)\;[0,4]\\(C)\;[0,3]&(D)\;[3,-4][\end{array}$
Interval [3,4]
Hence (A) is the correct answer.
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2018-02-19 09:45:34
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http://msp.ucsd.edu/techniques/latest/book-html/node149.html
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Next: All-pass filters Up: Designing filters Previous: Time-varying coefficients Contents Index
## Impulse responses of recirculating filters
In Section 7.4 we analyzed the impulse response of a recirculating comb filter, of which the one-pole low-pass filter is a special case. Figure 8.22 shows the result for two low-pass filters and one complex one-pole resonant filter. All are elementary recirculating filters as introduced in Section 8.2.3. Each is normalized to have unit maximum gain.
In the case of a low-pass filter, the impulse response gets longer (and lower) as the pole gets closer to one. Suppose the pole is at a point (so that the cutoff frequency is radians). The normalizing factor is also . After points, the output diminishes by a factor of
where is Euler's constant, about 2.718. The filter can be said to have a settling time of samples. In the figure, for part (a) and for part (b). In general, the settling time (in samples) is approximately one over the cutoff frequency (in angular units).
The situation gets more interesting when we look at a resonant one-pole filter, that is, one whose pole lies off the real axis. In part (c) of the figure, the pole has absolute value 0.9 (as in part b), but its argument is set to radians. We get the same settling time as in part (b), but the output rings at the resonant frequency (and so at a period of 10 samples in this example).
A natural question to ask is, how many periods of ringing do we get before the filter decays to strength ? If the pole of a resonant filter has magnitude as above, we have seen in Section 8.2.3 that the bandwidth (call it ) is about , and we see here that the settling time is about . The resonant frequency (call it ) is the argument of the pole, and the period in samples of the ringing is . The number of periods that make up the settling time is thus:
where is the quality of the filter, defined as the center frequency divided by bandwidth. Resonant filters are often specified in terms of the center frequency and q" in place of bandwidth.
Next: All-pass filters Up: Designing filters Previous: Time-varying coefficients Contents Index
Miller Puckette 2006-12-30
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2020-02-28 13:07:55
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http://crypto.stackexchange.com/questions?page=1&sort=newest
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# All Questions
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### Winternitz checksum
I'm reading the One Time Signature Winternitz in this book [pag 38]. My question is Why is important the checksum? Is there any attack again Winternitz OTS if the checksum is hidden?
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I’m implementing some file encryption module with random-access capability and AES-CTR seems the right way to go. I understand that reusing Keys and IVs can expose the file to ‘Stream Cipher Attacks’ ...
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### Survey: What papers are essential to read for a new crypto Ph.D student? [on hold]
this is a survey question, asking what papers are essential, in the sense that a) they are too good to miss and b) they are fundamental for understand current development of cryptography for a new ...
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71 views
### How can I show that the DDH problem is self-reducible?
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79 views
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### Linear Cryptanalysis - possible without plaintext?
If Linear Cryptanalysis exploits the fact that the plaintext and ciphertext are not completely unrelated, is the attack possible without having access to the plaintext?
29 views
### Semantic Security Active or Passive attacks?
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71 views
### How to best mix two arbitrary/random n-bit words?
Given two arbitrary/random $n$-bit words, how could one best mix them to get one $n$-bit word for general crypto usages? I suppose that one should have an adequate measure of goodness of the mix ...
34 views
### What is the “purpose” byte in Crypto++ PBKDF2?
Does anyone know the purpose of the "purpose" byte in the PBKDF2 implementation in Crypto++? It appears that the PBKDF2 does not use this byte, but I want to make sure I am not setting the option to ...
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2014-03-16 08:18:16
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https://ondm2021.chalmers.se/preparation-of-your-final-manuscript/
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# Preparation of Your Final Manuscript
The final camera-ready manuscript of your paper should account for all the critical reviewers’ feedback. Please be advised that your manuscript should strictly comply with the very same paper template specified at the submission phase. Please note that the final papers are limited to either 3 pages (short paper) or 6 pages (regular paper), and you will not be able to pay over-length charges for the extra pages. The following steps are required for successful final submission:
• Xplore compliance check PDF
• Completed and signed IFIP copyright form (PDF)
### Insertion of the IFIP Copyright Clearance Code Notice
The appropriate copyright clearance code notice is to appear on the bottom of the first page of each paper.
#### For Latex documents use:
\usepackage[pscoord]{eso-pic}
\newcommand{\placetextbox}[3]{
\setbox0=\hbox{#3}
\put(\LenToUnit{#1\paperwidth},\LenToUnit{#2\paperheight}){
\vtop{{\null}\makebox[0pt][c]{#3}}}
}
}
\placetextbox{.2}{0.055}{ 978-3-903176-33-1~\copyright~2021 IFIP}
#### For Microsoft Word documents use:
Microsoft Word users can use: ‘Insert’ -> ‘Textbox’, insert the appropriate copyright notice in the textbox, and place the box (without border) at the bottom left on the first page.
Further important requirements:
• The title is set in 24 pt non-bold
• Any running headers/footers or page numbers must be removed
• Columns should be balanced, i.e. have the same length on each page
• Blue-underlining for URLs and email addresses should be removed
• Papers must be in US-Letter size. A4 or other sizes are not allowed
Please note that you should prepare the final manuscript with no page numbering.
### Validation of Your Manuscript by PDF eXpress
• Go to IEEE PDF eXpress Website.
• Create an IEEE PDF eXpress account (use conference ID: 51796X). (Not later than 11 June 2021 23:59 CEST)
• Use ‘new user’ if you haven’t used this site before.
Use IEEE PDF eXpress to check if your PDF file is Xplore-compliant, OR, else, you can use this site to convert your source files into an IEEE Xplore-compliant PDF file (e.g., for LaTeX users, create a zip file that includes dvi and your eps figure files altogether, and then upload the zip file for the system to convert into a compliant PDF file; for MSWord users, upload the Word file and let it convert and return a compliant PDF file).
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2021-06-19 21:02:29
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https://zbmath.org/authors/?q=ai%3Aroberts.john-e.1
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# zbMATH — the first resource for mathematics
## Roberts, John E.
Compute Distance To:
Author ID: roberts.john-e.1 Published as: Roberts, J. E.; Roberts, John; Roberts, John E. External Links: MGP
Documents Indexed: 59 Publications since 1966, including 1 Book Biographic References: 1 Publication
all top 5
#### Co-Authors
18 single-authored 20 Doplicher, Sergio 8 Pinzari, Claudia 7 Buchholz, Detlev 6 Longo, Roberto 3 Haag, Rudolf 3 Morchio, Giovanni 3 Ruzzi, Giuseppe 3 Strocchi, Franco 2 Ghez, P. 2 Tuset, Lars 2 Vasselli, Ezio 2 Zsidó, Lászlo 1 Ceccherini, Tullio G. 1 Conti, Roberto 1 Druhl, K. J. 1 Fredenhagen, Klaus 1 Guido, Daniele 1 Leyland, Paul C. 1 Lima, Renan 1 Lima, Rui 1 Lüders, Christian 1 Müger, Michael 1 Roepstorff, Gert 1 Verch, Rainer
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#### Journals
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2018-12-14 06:52:33
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https://orbiter-forum.com/threads/implementing-a-key-press-release-to-toggle-surface-friction-coefficients.40628/#post-599002
|
# API QuestionImplementing a Key Press/Release to Toggle Surface Friction Coefficients
#### Thunder Chicken
Donator
I have been working on an air-breathing jet engine model for Orbiter, and have been using Kev33's Mirage2000 add-on model basically as a test bed to flight test that model. While doing so, I am trying to polish up some of the other functionality of that particular add-on, for self amusement if nothing else.
One thing I am trying to do is enable sensible steering and braking behavior while taxiing, which I know is a challenge with the current API tools. I've found that SetSurfaceFrictionCoeff, SetMaxWheelbrakeForce, and SetNosewheelSteering don't play well with each other at all.
As an example, if you set touchdown points and want to have them behave like a freely rotating wheel, you might set the friction coefficients like this example:
SetSurfaceFrictionCoeff(0.01, 1);
This makes resistance in the longitudinal direction small (rolling wheel), but high laterally (so the wheels don't scrub sideways).
This is all well and good, until you want to apply the brakes or steer. I've done some experimentation with SetMaxWheelbrakeForce, which the API reference says applies a specified brake force in Newtons, but it actually appears to be modified by the longitudinal friction coefficient set by SetSurfaceFrictionCoeff.
The Problems
Braking
So let's say you set the friction coefficients as I did above, and want to specify a braking force of 1000 N. You would think that SetMaxWheelbrakeForce(1000) would deliver 1000 N of braking force when SetWheelBrakeLevel to 1. But what you actually get is 1000 N * 0.01 = 10 N. It's roughly akin to locking up your car brakes on an icy road. So brakes are rendered effective.
Steering
You get the reverse problem when you attempt to use nose wheel steering with the SetNoseWheelSteering function. This applies a lateral steering force to the nose wheel in order to push it left or right based on yaw inputs. But if you specify the surface friction coefficients as I did above to prevent side slipping of the wheels, this actively opposes the nose steering forces. So nose wheel steering is rendered ineffective as well.
Potential Fixes
The braking issue by itself isn't too hard to fix - you could leave the longitudinal friction coefficient alone and just make your braking force 100 times higher (using my example numbers) to deliver the correct braking force. Most folks do this and call it a day.
But that still leaves you with steering problems. If you leave the lateral friction coefficient at 1 to prevent side slipping, it overwhelms the nose steering forces (which, as far as I can tell, are not possible to change or override like the brake forces).
What I am trying to do
So what I am trying to do to beat these issues is to implement differential braking and forgo the use of nose wheel steering, but change the surface friction coefficients when I apply the brakes to enable effective braking and steering. In SetClassCaps I have this entered:
C++:
SetSurfaceFrictionCoeff(0.01, 1.0);
SetMaxWheelbrakeForce(empty_mass * 2.0 * 9.81); //should provide ~2 G braking acceleration
This sets the friction coefficients to mimic a rolling wheel, and sets the brake force to a sensible nominal value. However, I know this won't work as-is for the above reasons. To fix this, in clbkConsumeBufferedKey I have modified the , and . keys to apply brakes like this:
C++:
case OAPI_KEY_COMMA: //Apply left wheel brake using Orbiter default brake key
{
//Increase longitudinal friction so brakes work, but lower lateral friction so nose turns
//Need to reset these coefficients when key is release to mimic rolling wheels.
SetSurfaceFrictionCoeff(1.0, 0.01);
//Apply the brake
SetWheelbrakeLevel(1, 1, false);
return 1;
}
case OAPI_KEY_PERIOD: //Apply right wheel brake using Orbiter default brake key
{
//Increase longitudinal friction so brakes work, but lower lateral friction so nose turns
//Need to reset these coefficients when key is release to mimic rolling wheels.
SetSurfaceFrictionCoeff(1.0, 0.01);
//Apply the brake
SetWheelbrakeLevel(1, 2, false);
return 1;
}
Note that this increases the longitudinal friction coefficient to 1.0 (to enable full braking force application), but also reduces the lateral friction coefficient (to allow the nose wheel to slide sideways).
This works, but I need to restore the surface friction coefficients to their original values when I release the brake keys. Right now I am brute forcing it by this bit of code in clbkPreStep:
C++:
if (GroundContact() == true)
{
SetSurfaceFrictionCoeff(0.01, 1.0);
}
This works, but it's obviously clunky as the code has to keep resetting the coefficients each time step, whether needed or not.
The Question
So, the question is, is there a way that I can simply restore the surface coefficients once when I release a key? In pseudo code I'm dreaming for something like this:
Code:
if (key pressed)
SetSurfaceFrictionCoeff(1.0, 0.01); //set up to brake and steer effectively
SetWheelBrakeForce(1,1); //I have this bit sorted out
if (key released)
SetSurfaceFrictionCoeff(0.01, 1.0); //resume free rolling wheel behavior
Is there a way to use the key release as a trigger to resume the normal coefficients like this?
#### Thunder Chicken
Donator
Actually, I'm still not sure what the SetBrakeLevel function does. Some simple timed braking tests don't seem to show any change in braking force due to it.
If I set the friction coefficient to 1 and disable SetWheelBrakeLevel, I'd expect a braking force equal to the weight of the aircraft, which should yield a braking deceleration of 1 g or -9.81 m/s2. So, if I ran the jet up to 100 m/s and slammed on the brakes I'd expect to stop in t = v0/a ~ 10-11 seconds. In practice it takes nearly 30 seconds to come to a halt.
If I set the friction coefficient to 0 and apply a braking force equal to the weight of the aircraft, I'd also expect to come to a halt from 100 m/s in about 10-11 seconds. But again, in practice it takes nearly 30 seconds to come to a halt?
Just for laughs, I disabled friction and braking forces in my addon and did this experiment, and I get exactly the same behavior! There seems to be some default Orbiter braking force associated with the , and . keys that completely ignores the addon brake and friction settings? What is going on? What is the point of having these API functions?
Last edited:
#### BrianJ
Hi,
just a thought - which method are you using to define your touchdown points? Is it possible that the SetSurfaceFrictionCoeff(...) function only applies to the old way of setting touchdown points (three vectors) - not the new way using a touchdown vertex array? Sounds like there are more than one issue here, anyway. Good luck!
BrianJ
#### GLS
##### Well-known member
Orbiter Contributor
Just putting here my knowledge of the brake functions: some years ago I noticed that the argument of SetMaxWheelbrakeForce() didn't work as the braking force was always the same (this was posted in a ticket in the old forum). Since then, the Orbiter sources went public and I've spent just a couple of minutes looking into this, and it seems the new touchdown system doesn't use the parameter passed by SetMaxWheelbrakeForce().
I managed to bypass the default brake keys, by "eating" them in clbkConsumeDirectKey() with the RESETKEY macro. I could then "integrate" the key presses and have a linear rise and fall to the braking, instead of the default "on or off" way, and then call SetWheelbrakeLevel() with my "integrated" value. As I was having too much brake force, I added a <1 factor to decrease the value passed to SetWheelbrakeLevel(), so the resulting braking force is +/- what I need.
#### Thunder Chicken
Donator
I am using the old 3-point contact model with SetSurfaceFrictionCoefficient for now. The friction coefficients are set inside the new vertex model. It does not appear that the new vertex model generates guess values of the spring coefficients as advertised, so it's just easier to deal with the old model.
The RESETKEY macro may be what I am missing to replace the braking function of the . and , keys. I still would like a better way of restoring the unbraked friction coefficients when the brake keys are released.
#### Thunder Chicken
Donator
The RESETKEY macro did the trick to let my braking model use the , and . keys.
One thing I have realized is that there is only a single definition of surface friction coefficient, and it appears to be for dynamic friction only. In general, for two contacting solid surfaces, there should be a static friction coefficient and a dynamic or kinetic coefficient. The static coefficient defines the frictional force needed to be overcome to get a stationary object to start to slide, and the dynamic coefficient defines the frictional force opposing the motion of a sliding object.
What this means is that any thrust force applied to a vessel in Orbiter will accelerate the vessel from rest, even if the brakes are fully applied. So it is impossible to model holding brakes and running up the engines without moving. Blah.
#### JMW
Just putting here my knowledge of the brake functions: some years ago I noticed that the argument of SetMaxWheelbrakeForce() didn't work as the braking force was always the same (this was posted in a ticket in the old forum). Since then, the Orbiter sources went public and I've spent just a couple of minutes looking into this, and it seems the new touchdown system doesn't use the parameter passed by SetMaxWheelbrakeForce().
I managed to bypass the default brake keys, by "eating" them in clbkConsumeDirectKey() with the RESETKEY macro. I could then "integrate" the key presses and have a linear rise and fall to the braking, instead of the default "on or off" way, and then call SetWheelbrakeLevel() with my "integrated" value. As I was having too much brake force, I added a <1 factor to decrease the value passed to SetWheelbrakeLevel(), so the resulting braking force is +/- what I need.
Hi All.
Where do you put the RESETKEY macro to disable default brake key ?
Have tried in clbkConsumeDirectKey but doesn't disable the regular COMMA / PERIOD function,
is still FULL ON/OFF.........
What am I missing ?
int ShuttlePB::clbkConsumeDirectKey (char *kstate) { RESETKEY (kstate, OAPI_KEY_COMMA); RESETKEY (kstate, OAPI_KEY_PERIOD); if (KEYDOWN (kstate, OAPI_KEY_COMMA &&!KEYMOD_SHIFT(kstate)&&!KEYMOD_CONTROL (kstate))) // Less Wheelbrake left { blevell += 0.000001; if (blevell > 0.4) { blevell = 0.4; } SetWheelbrakeLevel(blevell,1, false); return 1; } if (KEYDOWN (kstate, OAPI_KEY_PERIOD &&!KEYMOD_SHIFT(kstate)&&!KEYMOD_CONTROL (kstate))) // Less Wheelbrake right //if (blevelr == 0) { blevelr += 0.000001; if (blevelr > 0.4) { blevelr = 0.4; } SetWheelbrakeLevel(blevelr,2, false); return 1; } .............................................................
Last edited:
#### GLS
##### Well-known member
Orbiter Contributor
Hi All.
Where do you put the RESETKEY macro to disable default brake key ?
Have tried in clbkConsumeDirectKey but doesn't disable the regular COMMA / PERIOD function,
is still FULL ON/OFF.........
What am I missing ?
int ShuttlePB::clbkConsumeDirectKey (char *kstate) { RESETKEY (kstate, OAPI_KEY_COMMA); RESETKEY (kstate, OAPI_KEY_PERIOD); if (KEYDOWN (kstate, OAPI_KEY_COMMA &&!KEYMOD_SHIFT(kstate)&&!KEYMOD_CONTROL (kstate))) // Less Wheelbrake left { blevell += 0.000001; if (blevell > 0.4) { blevell = 0.4; } SetWheelbrakeLevel(blevell,1, false); return 1; } if (KEYDOWN (kstate, OAPI_KEY_PERIOD &&!KEYMOD_SHIFT(kstate)&&!KEYMOD_CONTROL (kstate))) // Less Wheelbrake right //if (blevelr == 0) { blevelr += 0.000001; if (blevelr > 0.4) { blevelr = 0.4; } SetWheelbrakeLevel(blevelr,2, false); return 1; } .............................................................
C++:
{
if (KEYDOWN(kstate, OAPI_KEY_COMMA))
{
RESETKEY(kstate, OAPI_KEY_COMMA);// prevent default processing of the key
// do things
}
else
{
// reset things
}
if (KEYDOWN(kstate, OAPI_KEY_PERIOD))
{
RESETKEY(kstate, OAPI_KEY_PERIOD);// prevent default processing of the key
// do things
}
else
{
// reset things
}
return 0;
}
#### Thunder Chicken
Donator
C++:
{
if (KEYDOWN(kstate, OAPI_KEY_COMMA))
{
RESETKEY(kstate, OAPI_KEY_COMMA);// prevent default processing of the key
// do things
}
else
{
// reset things
}
if (KEYDOWN(kstate, OAPI_KEY_PERIOD))
{
RESETKEY(kstate, OAPI_KEY_PERIOD);// prevent default processing of the key
// do things
}
else
{
// reset things
}
return 0;
}
I thought I understood what was going on, but now I think I don't. I thought you just ran RESETKEY in clbkConsumeDirectKey but then defined the key events as normal in clbkConsumeBufferedKey? In actuality, it is all done in clbkConsumeDirectKey for the keys that are being reset?
#### GLS
##### Well-known member
Orbiter Contributor
I thought I understood what was going on, but now I think I don't. I thought you just ran RESETKEY in clbkConsumeDirectKey but then defined the key events as normal in clbkConsumeBufferedKey? In actuality, it is all done in clbkConsumeDirectKey for the keys that are being reset?
Yeah, that is all in clbkConsumeDirectKey(). Maybe it works just eating the key there, and having the rest of the logic in clbkConsumeBufferedKey(), but I never tried it.
#### Thunder Chicken
Donator
Yeah, that is all in clbkConsumeDirectKey(). Maybe it works just eating the key there, and having the rest of the logic in clbkConsumeBufferedKey(), but I never tried it.
I'll have to try that. It seems that my braking action died when I tried using clbkConsumeBufferedKey().
#### JMW
C++:
{
if (KEYDOWN(kstate, OAPI_KEY_COMMA))
{
RESETKEY(kstate, OAPI_KEY_COMMA);// prevent default processing of the key
// do things
}
else
{
// reset things
}
if (KEYDOWN(kstate, OAPI_KEY_PERIOD))
{
RESETKEY(kstate, OAPI_KEY_PERIOD);// prevent default processing of the key
// do things
}
else
{
// reset things
}
return 0;
}
Hi there,
Still no joy with this, can't get it to disable default operation of the brakes.
Code:
// In
int ShuttlePB::clbkConsumeDirectKey (char *kstate)
{
if (KEYDOWN (kstate, OAPI_KEY_COMMA)) // Less Wheelbrake left
{
blevell += 0.000001;
if (blevell > 0.4) {
blevell = 0.4;
}
SetWheelbrakeLevel(blevell,1, false);
RESETKEY (kstate, OAPI_KEY_COMMA);
}
//return 0;
if (KEYDOWN (kstate, OAPI_KEY_PERIOD)) // Less Wheelbrake right
{
blevelr += 0.000001;
if (blevelr > 0.4) {
blevelr = 0.4;
}
SetWheelbrakeLevel(blevelr,2, false);
RESETKEY (kstate, OAPI_KEY_PERIOD);
}
//return 0;
}
return 0;
But this works - Disables default operation.
I don't get it
Code:
if (KEYDOWN (kstate, OAPI_KEY_NUMPAD2 ))
{
if(spotcntrl >-15)
{spotcntrl = spotcntrl - 0.51* oapiGetSimStep();
if(spotcntrl <-1.50)
spotcntrl = spotcntrl - 4.51* oapiGetSimStep();}
}
#### Thunder Chicken
Donator
I'd think the first code would work if you ran RESETKEY first, before trying to set your own braking model.
#### GLS
##### Well-known member
Orbiter Contributor
I'd think the first code would work if you ran RESETKEY first, before trying to set your own braking model.
This is probably it.
Also of note, my calls to SetWheelbrakeLevel() are clbkPostStep().
#### JMW
This is probably it.
Also of note, my calls to SetWheelbrakeLevel() are clbkPostStep().
Following your post if I understand correctly .......
In clbkConsumeDirectKey()
Code:
if (KEYDOWN (kstate, OAPI_KEY_COMMA)) // Less Wheelbrake left
{
RESETKEY (kstate, OAPI_KEY_COMMA);
if(CommaKey == 0) CommaKey = 1;
}
else { CommaKey = 0;}
if (KEYDOWN (kstate, OAPI_KEY_PERIOD)) // Less Wheelbrake right
{
RESETKEY (kstate, OAPI_KEY_PERIOD);
if(PeriodKey == 0) PeriodKey = 1;
}
else { PeriodKey = 0;}
}
return 0;
In clbkPostStep()
Code:
if (CommaKey == 1) // Less Wheelbrake left
{
blevell += 0.000001;
if (blevell > 0.4) {
blevell = 0.4;
}
SetWheelbrakeLevel(blevell,1, false);
}
if (PeriodKey == 1) // Less Wheelbrake right
{
blevelr += 0.000001;
if (blevelr > 0.4) {
blevelr = 0.4;
}
SetWheelbrakeLevel(blevelr,2, false);
}
Still doesn't disable default braking.........
#### Thunder Chicken
Donator
You need to read my original post at the top of this thread. It seems the maximum braking force you can get is limited by the friction coefficient in the direction of travel. The maximum braking force you can realistically get is (1.0) x vessel weight. It seems that the SetMaxWheelbrakeForce value is limited by the friction to (1.0) x vessel weight.
#### GLS
##### Well-known member
Orbiter Contributor
Still doesn't disable default braking.........
Even if you comment SetWheelbrakeLevel()?
#### Thunder Chicken
Donator
SetMaxWheelbrakeForce and SetWheelbrakeLevel don't work the way that you think they do. They are ultimately limited by the friction coefficient of the contact points.
My brake model doesn't use SetMaxWheelbrakeForce and SetWheelbrakeLevel at all anymore - it simply switches the friction coefficients of the contact points.
The friction drag force F exerted by the contact points is equal to mu * W, where mu is the dynamic friction coefficient and W is the total vessel weight. No matter your SetMaxWheelbrakeForce and SetWheelbrakeLevel settings, your braking force will never exceed mu * W. So if you have contact points that you want to have behave as rolling wheels, you need to set the longitudinal and lateral coefficients like this:
C++:
SetSurfaceFrictionCoeff(0.01, 1.0); //low friction in direction of motion (a rolling wheel)
But if you want to slow down the vessel, you need to increase the coefficient in the direction of travel. And if you want to steer using differential braking, you need to be able to let the nose wheel slide laterally, so you need to reduce the lateral coefficient, like this:
C++:
SetSurfaceFrictionCoeff(1.0, 0.01); //maximum friction in direction of motion (braking), but low laterally (for steering)
The upshot is - there is no way to apply a higher drag or braking force greater than the weight of the aircraft without resorting to AddForce. By itself this is OK as it is somewhat realistic. But sadly, the contact model does not provide a static friction coefficient capability, so you can't "lock up" the brakes like if you wanted to run up engines before take-off. Any thrust at all will cause the vessel to slide.
#### JMW
You need to read my original post at the top of this thread. It seems the maximum braking force you can get is limited by the friction coefficient in the direction of travel. The maximum braking force you can realistically get is (1.0) x vessel weight. It seems that the SetMaxWheelbrakeForce value is limited by the friction to (1.0) x vessel weight.
Thanks for your help with this.
I'm trying to get less braking effort, rather than the maximum, but whatever figure I put in SetWheelbrakeLevel() however low, always results in the same effect - maximum braking.
Even if you comment SetWheelbrakeLevel()?
Yes, still get the maximum braking effect even commenting out the whole chabang in clbkPostStep().
you can't "lock up" the brakes like if you wanted to run up engines before take-off. Any thrust at all will cause the vessel to slide.
So that's why it's not possible to keep stationary on an incline too, even with brakes applied ?
#### GLS
##### Well-known member
Orbiter Contributor
Yes, still get the maximum braking effect even commenting out the whole chabang in clbkPostStep().
Can you confirm that the code execution passes RESETKEY?
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2022-10-07 09:10:55
|
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|
https://physics.stackexchange.com/questions/349088/is-it-correct-to-say-energy-occurs-in-quanta-of-magnitude-frach2-pi
|
# Is it correct to say energy occurs in quanta of magnitude $\frac{h}{2\pi}$?
I read this thing in a book called Concise Inorganic Chemistry By JD Lee.It says-
According to Planck's quantum theory,energy is not continuous but is discrete.This means that energy occurs in 'packets' called quanta, of magnitude $\frac{h}{2\pi}$.The energy of an electron in an orbit, ie. its angular momentum $mvr$, must be eqaul to a whole number $n$ of quanta.
Now,I knew that $E$ is multiple of $h\nu$.But why does this book say $\frac{h}{2\pi}$?Is this correct?
• That is not correct. And energy is not angular momentum. Those errors make the entire book suspect. Jul 28 '17 at 18:15
• @garyp Yeah...But the book seemed quite standard... because the 'About the author' part says-"Senior Lecturer in Inorganic Chemistry at Loughborough University"... Jul 28 '17 at 18:17
• That is the reduced Planck constant, also known as hbar. It crops up as much as h itself, and if we could go back in time,we would probably use it rather than h
– user163104
Jul 28 '17 at 18:17
• $h\nu$ = $\hbar \omega$. Most equations are easier in $\omega$... Jul 28 '17 at 18:18
• Despite the author's credentials, he is wrong. Where were the editors? Jul 28 '17 at 18:18
This is a gross and incorrect generalization of a thing that is true in a limited sense.
It is true that bound quantum systems exhibit discrete eigenenergies.
It is true that for systems with a harmonic potential those discrete energies are separated by a fixed and constant amount of energy $h\nu = \hbar \omega$ where $\nu$ ($\omega$) is the frequency (angular frequency) of the system (harmonic potentials also have the property that this frequency is the same for all bound states).
It is not, however, true that all systems are bound, nor that all systems interact with harmonic potentials, nor that all harmonic systems have a unit angular frequency.
So
• Some systems are free and exhibit continuous spectra.
• Some bound systems are non-harmonic and exhibit non-constant spacing between discrete levels.
• Some harmonic systems have different step sizes.
No. The statement is nonsensical because $h/(2\pi)$ does not have units of energy - it has units of energy times time. It makes no sense for energy to come in units of something that isn't an energy.
Also, energy does not come in little units of anything. Physics is Lorentz-invariant. This means that if you have a photon of some energy $E$, you can shift into another reference frame and give the photon any energy you want. All energies are allowed. The book is wrong.
Regarding orbitals, the energy of an electron in a Hydrogen-like atom (only one electron) in SI units is
$$E_n = \frac{Z^2me^4}{8 n^2 h^2\epsilon_0^2}$$
where $Z$ is the atomic number, $m$ the electron mass, $e$ the electron charge, $h$ Planck's constant, and $\epsilon_0$ the permittivity of free space. As you can see, the energy does not come in units of $h/(2\pi)$, and this is only the simplest case; it ignores multiple electrons and other effects such as magnetism.
Also, angular momentum and energy are not the same thing, as the passage you quoted implies.
It appears the author simply used the word "energy" where they should have used the words "angular momentum".
In the Bohr model, angular momentum was hypothesized to come only in units of $h/(2\pi)$. This is not exactly the entire story, see this link on Wikipedia for more.
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2022-01-22 20:38:27
|
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https://notes.eonu.net/topics/discrete-maths/trees/notes.html
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## Trees
A tree is a connected simple undirected graph with no simple circuits.
A forest is a (not necessarily connected) simple undirected graph with no simple circuits.
### Theorems
A graph $G$ is a tree iff there is a unique simple path between any two vertices of $G$.
Every tree, $T=(V,E)$ with $|V| \geq 2$, has at least two vertices that have degree 1.
Every tree with $n$ vertices has exactly $n-1$ edges.
### Rooted trees
A rooted tree is a pair $(T,r)$ where $T=(V,E)$ is a tree, and $r \in V$ is a chosen root vertex of the tree. Often, the edges of a rooted tree are viewed as being directed:
For each node $v \neq r$ the parent is the unique vertex $u$ such that $(u,v) \in E$. $v$ is then called a child of $u$. Two vertices with the same parent are called siblings.
A leaf is a vertex with no children. Non-leaves are called internal vertices. In the example above, $f, g, d, e$ are leaves.
The height of a rooted tree is the length of the longest directed path from the root to any leaf. In the example above, the height of the graph is $2$.
The ancestors of a vertex $v$ are all vertices $u \neq v$ such that there is a directed path from $u$ to $v$. In the example above, the ancestors of $b$ are $a$ and $c$.
The descendants of a vertex $v$ are all vertices $u \neq v$ such that there is a directed path from $v$ to $u$. In the example above, the descendants of $c$ are every other vertex in the graph.
The subtree rooted at $v$, is the subgraph containing $v$ and all its descendants, and all directed edges between them.
## $m$-ary trees
For $m \geq 1$, a rooted tree is called a $m$-ary tree if every internal node has at most $m$ children.
It is called a full $m$-ary tree if every internal node has exactly $m$ children.
An $m$-ary tree with $m=2$ is called a binary tree.
$T_1, T_2, T_3$ are full binary, 3-ary and 5-ary trees (respectively). $T_4$ is a non-full 3-ary tree, as not every internal node has exactly 3 children.
Note that the root node is considered an internal node.
### Counting vertices
#### Theorems
$\forall m \geq 1$, every full $m$-ary tree with $i$ internal vertices has exactly $n=m \cdot i+1$ vertices.
Proof: Every vertex other than the root is a child of an internal vertex. There are thus $m \cdot i$ such children, plus $1$ root.
$\forall m \geq 1$ a full $m$-ary tree with:
1. $n$ vertices has $i=(n-1)/m$ internal vertices and $l=[(m-1)n+1]/m$ leaves.
2. $i$ internal vertices has $n=m \cdot i+1$ vertices and $l=(m-1)i+1$ leaves.
3. If $m \geq 2$, then if the $m$-ary tree has $l$ leaves then it has $n=(ml-1)/(m-1)$ vertices and $i=(l-1)/(m-1)$ internal vertices.
Proof: All of these can be derived from $n=l+i$ and $n=m \cdot i+1$.
There are at most $m^h$ leaves in an $m$-ary tree of height $h$.
Proof: By induction on $h \geq 0$.
If an $m$-ary tree has $l$ leaves, and $h$ is its height, then $h \geq \lceil \log_m l \rceil$.
Proof: Since $l \leq m^h$, we have $\log_m l \leq h$. But $h \in \mathbb{Z}^+$, so $\lceil \log_m l \rceil \leq h$.
## Spanning trees of undirected graphs
For a simple undirected graph $G$, a spanning tree of $G$ is a subgraph $T$ of $G$ such that $T$ is a tree and $T$ contains every vertex of $G$.
The blue heavy edges in this grid graph represent a spanning tree.
### Theorems
Every connected graph $G$ has a spanning tree.
Proof: While there is a circuit in $G$, remove one edge of the circuit. Repeat until there are no more circuits. Removing one edge of the circuit does not change connoectivity, and eventually no circuits can remain (because there are finitely many edges to be removed). So the end result is a tree which is a subtree of $G$.
## Prim's algorithm
Prim's algorithm finds a minimum spanning tree for a weighted undirected graph. This means it find a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.
Hegarty Maths
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2020-10-28 16:42:25
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https://ltwork.net/plzzz-donr-be-mean-i-know-this-isnt-the-sit-for-this-but--900
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# Plzzz donr be mean. i know this isnt the sit for this but i need yall points of view plz. ra te me, my stomache, and my biceps 1-10
###### Question:
plzzz donr be mean. i know this isnt the sit for this but i need yall points of view plz. ra te me, my stomache, and my biceps 1-10 thxs
$plzzz donr be mean. i know this isnt the sit for this but i need yall points of view plzzzz. ra te$
$plzzz donr be mean. i know this isnt the sit for this but i need yall points of view plzzzz. ra te$
$plzzz donr be mean. i know this isnt the sit for this but i need yall points of view plzzzz. ra te$
$plzzz donr be mean. i know this isnt the sit for this but i need yall points of view plzzzz. ra te$
### In “The legend of sleepy hollow” the way Katrina’s parents raised her, what makes her a coquette?
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2023-01-30 20:38:53
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https://socratic.org/questions/how-do-you-find-the-slope-for-a-2-6-b-4-7
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# How do you find the slope for A(2,6) B(4,7)?
Jul 17, 2016
The slope equals $m = \frac{1}{2}$
#### Explanation:
Slope which is the change in $x$ versus the change in $y$.
Slope is identified by the letter $m$
$m = \frac{\Delta y}{\Delta x}$
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
$\left(2 , 6\right)$ and $\left(4 , 7\right)$
${x}_{1} = 2$
${y}_{1} = 6$
${x}_{2} = 4$
${y}_{2} = 7$
$m = \frac{7 - 6}{4 - 2}$
$m = \frac{1}{2}$
The slope equals $m = \frac{1}{2}$
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2022-10-05 16:10:47
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https://ch.gateoverflow.in/520/gate-chemical-2017-question-3
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The number of positive roots of the function $f(x)$ shown below in the range $0<x<6$ is ___________________.
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2022-05-27 23:01:21
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http://clay6.com/qa/49194/two-dice-are-thrown-the-events-a-b-and-c-are-as-follows-a-getting-an-even-n
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Browse Questions
# Two dice are thrown.The events A,B and C are as follows :A : getting an even number in first die,B : getting an odd number on the first die,C : getting the sum of the numbers on the dice $\leq$ 5.State true or false : A',B' and C are mutually exclusive & exhaustive
$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array}$
Given two dice are thrown
Possible outcomes =$6\times 6=36$
$\therefore$ The sample space
$S=\left\{\begin{array}{1 1}(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)\\(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\\(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)\\(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)\\(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)\\(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)\end{array}\right\}$
A: Getting an even number on first die
A': Getting an odd number on first die
B': Getting an even number on first die
C:Getting the sum of the numbers on the dice $\leq 5$
$A' \cap B'=\phi$
But $A'\cup B' \cap C=S$
$A'\cap C=B\cap C=\{(1,1),(1,2),(1,3),(1,4),(3,1),(3,2)\}\neq \phi$
$B'\cap C=A\cap C=\{(2,1),(2,2),(2,3),(4,1\}\neq \phi$
$\therefore A',B'$ and $C$ are not mutually exclusive but exhaustive.
Hence the given statement is False.
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2017-01-24 17:25:27
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https://brilliant.org/problems/oh-wait-wind-disturbed-question/
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# Oh, wait wind disturbed question.
Classical Mechanics Level 5
Two cyclists, Mike and Josh, simultaneously started toward each other from two town $$D$$ apart. Josh rode at $$v_{j}$$, and Mike rode at $$v_{m}$$. Before departure, a fly landed on Josh's nose and started to fly toward Mike the moment Josh departs. When it reached Mike, it immediately turned back and flew towards Josh. As soon as the fly reached Josh, it turned back again, and so on. Air speed of fly was always $$v_{f}$$ and the wind blew always toward Mike with constant velocity $$v_{w}$$. Find the total distance $$S$$ flown by the fly until the cyclists met.
Details:
• $$D$$=$$24 km$$ , $$v_{j}$$=$$25 km/h$$ , $$v_{m}$$=$$15 km/h$$ , $$v_{f}$$=$$30 km/h$$ , $$v_{w}$$=$$10 km/h$$
• $$S$$ is in $$km$$
• Gravity is ignored in every aspect.
• The problem is from physics olympiad.
×
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2016-10-27 03:03:20
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http://www.thestudentroom.co.uk/wiki/Maths_A_Level_S2
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• # Maths A Level S2
TSR Wiki > Study Help > Subjects and Revision > Mathematics > Mathematics A Level > Maths A Level S2
## Conditions for a Binomial Distribution
1. There must be a fixed number of trials.
2. Trials must be independant.
3. The trials must have 2 outcomes, success or failure.
4. The probability of success must be constant for every trial.
## Conditions for a Poisson Distribution
Events occur independantly, at a constant rate, and singly in continuous space or time.
## Approximations using different Distributions
1. Poisson approximation to Binomial Distribution: Can be used when n (no. of trials) is large (>75) and when p (probability of success) is small. Po(np) is used.
2. Normal approximation to Binomial Distribution: N(np, np(1-p)) can be used when n is large and p is close to 0.5.
3. Normal approximation to Poisson Distribution: Can be used when lambda is greater than 10. Mean = variance = lambda
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2014-04-25 03:12:50
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https://discuss.codechef.com/t/subtask-problem/22237
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#1
hi, I am new to competitive programming. i have solved some of basic questions but i face problems in each and every question where there are subtasks. like in this problem,
Constraints
1≤T≤1,000
1≤N≤1018
N does not contain the digit 0
1≤d≤9
1≤T≤100
1≤N≤109
Subtask #2 (60 points): original constraints
i found difficulty when there are 2 different ranges for a single variable i.e subtask.
can you please help me out to understand how to score in these questions and submit successfully.
#2
The ranges for a variable are its upper and lower limits in the input. For example, if there is an array which has N elements, and 1$\leq$N$\leq10^5$, it means that in the input, the array will have atleast 1 and atmost 10^5 elements. This helps us in estimating the Time Complexity that our program, to solve the problem, must have. You can learn more about this here. For other general queries, you can refer to this.
The purpose of subtasks is to let algorithms of certain Time Complexity pass, and others, not.
For example, consider a problem in which you have to deal with N numbers, and there are two subtasks -
1. 1 \leq N \leq 10^3
2. 1 \leq N \leq10^5
For the first subtask, our program will successfully run even if it has a Time Complexity of O(N^2), while for the second one it won’t. For the second subtask, we’ll need to use a faster algorithm. Thus, if you are able to pass a certain subtask, you’ll get the points for that subtask.
Problems which have a number of test cases T in the input, for them, the final complexity is O(T*worst case complexity of individual test case).
Feel free to ask if you have any doubts
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2019-04-22 00:13:18
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https://www.gradesaver.com/textbooks/math/algebra/algebra-and-trigonometry-10th-edition/chapter-4-4-4-translations-of-conics-4-4-exercises-page-348/46
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## Algebra and Trigonometry 10th Edition
Center: $(6,-7)$ Foci: $(6,-7+2\sqrt 3)~~and~~(6,-7-2\sqrt 3)$ Vertices: $(6,-2)~~and~~(6,-11)$
The standard form of the equation of the elipse when the major axis is: - horizontal: $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ in which $(h,k)$ is the center and $2a$ is the major axis length and $2b$ is the minor axis length. - vertical: $\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$ in which $(h,k)$ is the center and $2a$ is the major axis length and $2b$ is the minor axis length. $\frac{(x-6)^2}{4}+\frac{(y+7)^2}{16}=1$ $\frac{(x-6)^2}{2^2}+\frac{(y+7)^2}{4^2}=1$ $\frac{(x-6)^2}{2^2}+\frac{[y-(-7)]^2}{4^2}=1$ $a=4,~~b=2$ $c^2=a^2-b^2=16-4=12$ $c=2\sqrt 3$ Center: $(6,-7)$ The major axis is vertical: - the foci: $(6,-7+2\sqrt 3)~~and~~(6,-7-2\sqrt 3)$ - the vertices: $(6,-6+4)=(6,-2)~~and~~(6,-7-4)=(6,-11)$
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2022-12-06 11:15:06
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https://academy.vertabelo.com/course/python-strings/string-basics/quick-recap/strings-in-python
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Introduction
Quick recap
2. Strings in Python
Indexing and slicing
Summary
## Instruction
In Python, strings are text values in single ('sample text') or double quotes ("sample text"). There is no difference between these two notations; whichever you use, simply try to stay consistent. In this course, we'll stick to single quotes.
greeting = 'Hello, world!'
print(greeting)
The code above creates a new variable named greeting and prints its value to the output.
## Exercise
Create a variable named species with the following content: Aspidites melanocephalus
### Stuck? Here's a hint!
Remember to put the content inside single quotes.
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2019-01-16 14:55:23
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http://www.physicsforums.com/showthread.php?p=3764829
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# Help with Integrating Factor
by hurcw
Tags: factor, integrating
P: 20 I am really struggling with proving a ODE by means of using the integrating factor method. My original problem was a Laplace transform q'+2q=5sin(t) where q(0)=0 I believe i have got the correct naswer for this as being:- q= e^-2t +2sint-cost I just need to confirm this i have my integrating factor as e^2x but after that i am not really sure where to go next. I am surrounded by piles of paper with varying answers on, non of which are the same as the one above. Please please help someone.
HW Helper
Thanks
P: 26,148
hi hurcw! welcome to pf!
(try using the X2 button just above the Reply box )
Quote by hurcw q'+2q=5sin(t) where q(0)=0 … i have my integrating factor as e^2x but after that i am not really sure where to go next.
yes, you multiply the orignal equation by e2t, giving:
e2tq' +2qe2t = 5e2tsin(t)
that's the same as:
(qe2t)' = 5e2tsin(t)
now you integrate both sides:
qe2t = ∫ 5e2tsin(t) dt
and finally multiply the RHS (after the integration, and don't forget the constant!) by e-2t, to give you q
P: 20 Thanks for the reply if i integrate 5e^2t sin(t) do i not just get the same +C, and then if i multiply by e-2t it cancels out the e2ttso i am left with 5sin(t)+ C. Or am i being completely retarded which is a major possibility
HW Helper
Thanks
P: 26,148
Help with Integrating Factor
Quote by hurcw Thanks for the reply if i integrate 5e^2t sin(t) do i not just get the same+C …
nooo
d/dt(5e2tsint) = 10e2tsint + 5e2tcost
P: 20 Ahhh i see.....i think, I then multiply this by e(-2t) Which cancels out the e(2t) am i right? i still dont see how i end up at my original answer?
HW Helper
Thanks
P: 26,148
Quote by hurcw … i still dont see how i end up at my original answer?
show us what you've done
P: 20 Right here it is:- q'+2q=5sin(t) IF= e(2t) , Q=5sin(t) e(2t)q'+2e(2t)q=5e(2t)sin(t) d/dt2(e(2t)q)=5e(2t)sin(t) 2(e(2t)q)=∫5e(2t)sin(t).dt = 10e(2t)sin(t)+5e(2t)cos(t)+C e(2t)q=(5(2e(2t)sin(t)+e(2t)cos(t))+C/2 q=(5(2e(2t)sin(t)+e(2t)cos(t))+C/2e(2t) I then put in my original boundary condition of q(0)=0 to find C And end up with C=-5 which kind of tallies up because q = 10e(2t)sin(t)+5e(2t)cos(t)+C 0 = (0x1)+(5x1)-5 Transposed 5 = 5 Hows this look so far ??
HW Helper
Thanks
P: 26,148
(just got up …)
Quote by hurcw q'+2q=5sin(t) IF= e(2t) , Q=5sin(t) e(2t)q'+2e(2t)q=5e(2t)sin(t) d/dt2(e(2t)q)=5e(2t)sin(t) 2(e(2t)q)=∫5e(2t)sin(t).dt = 10e(2t)sin(t)+5e(2t)cos(t)+C
no, that last line is wrong …
if you differentiate it, you don't get 5e(2t)sin(t)
(also, that "2" on the far left came from nowhere)
P: 20 The '2' is from the original 2q. I don't get what you mean about my differentiation at the end, i have not differentiated yet. Where am i going wrong ? So is it this line that is wrong? q=(5(2e(2t)sin(t)+e(2t)cos(t))+C/2e(2t) Should it be q=5(2e(2t)sin(t)+e(2t)cos(t))+C/e(2t) which would cancel down to q=5(e(2t)sin(t)+cos(t))+C wouldn't it ?????
P: 20 Can anyone offer any more assistance with his please, all the help so far has been greatly appreciated.
HW Helper
Thanks
P: 26,148
hmm … let's rewrite that so that it's readable …
q=(5(2e2tsin(t)+e2tcos(t))+C/2e2t) Should it be q=5(2e2tsin(t)+e2tcos(t))+C/e2t which would cancel down to q=5(e2tsin(t)+cos(t))+C
no your ∫ was wrong (there should be a minus in the first line),
and because you've put your brackets in the wrong place, there are errors in the next two lines also
you must write these proofs out more carefully and in full (ie without taking short-cuts by missing out lines)
Related Discussions Differential Equations 4 Calculus & Beyond Homework 14 Differential Equations 4 Calculus & Beyond Homework 2 Introductory Physics Homework 2
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2014-08-22 02:05:03
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https://www.physicsforums.com/threads/verify-stokes-theorem-for-f-across-a-paraboloid.603730/
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# Homework Help: Verify Stokes' Theorem for F across a paraboloid
1. May 6, 2012
### jerzey101
1. The problem statement, all variables and given/known data
Verify Stokes' Theorem for F(x,y,z)=(3y,4z,-6x) where S is part of the paraboloid z=9-x2-y2 that lies above the xy-plane, oriented upward.
2. Relevant equations
Stokes' Theorem is ∫F*ds=∫∫scurl(F)*ds
Where curl(F)=∇*F
3. The attempt at a solution
I got curl(F)=(-4,6,-3)
then I'm not sure what to do. my notes say to parameterize s and then compute the normal vector n, then compute ∫∫curl(F)*n. I'm not sure how to parameterize z=9-x2-y2.
2. May 6, 2012
### sharks
Since $\hat n$ is the outward normal unit vector, directed upwards, above the plane z=0, the $\vec k$ vector component must be positive. Hence: $\phi (x,y,z)=x^2+y^2+z-9$
Now, to find $\hat n$, just use the formula:
$$\frac{∇\vec \phi}{|∇\vec \phi|}$$
You have found $∇\times \vec F=-4\hat i+6\hat j-3\hat k$
Now, all you have to do, is just project the surface S onto the x-y plane and find the area.
3. May 6, 2012
### jerzey101
So (2x,2y,1) / sqrt(4x2+4y2+1)
how do you go about simplifying this?
4. May 6, 2012
### sharks
You can't simplify the square root at this point. Just proceed by multiplying with Curl F and find the surface area.
5. May 6, 2012
### jerzey101
so -8x + 12y - 3 all over [itex]\sqrt{4x2+4y2+1}[\itex]
I'm sorry, I am so lost with this one.
And I am doing battle with the formatting. I don't get why it's not working
Last edited: May 6, 2012
6. May 6, 2012
### sharks
To close the itex tag, always use backslash \ instead of /
Your expression is correct. Now, project the surface to find the surface area.
7. May 6, 2012
### jerzey101
Meaning integrate it over the paraboloid?
8. May 6, 2012
### sharks
Read the last line of post #2.
9. May 6, 2012
### LCKurtz
When you are calculating a flux integral over a surface $S$$$\iint_S \vec F\cdot d\vec S=\iint_S\vec F \cdot \hat n dS$$you parameterize the surface in convenient variables $u$ and $v$ (which may be just $x$ and $y$)$$\vec R = \vec R(u,v)$$The normal to the surface is $\pm \vec R_u\times \vec R_v$, with the sign chosen to agree with the orientation. Then to get a unit normal you have$$\hat n =\pm \frac{\vec R_u\times \vec R_v}{|\vec R_u\times\vec R_v|}$$The scalar $dS\$is given by$$dS=|\vec R_u\times \vec R_v|dudv$$When you put these in the formula for the flux integral you get$$\iint_S \vec F\cdot d\vec S=\iint_S\vec F \cdot \hat n dS= \pm\iint_{(u,v)}\vec F\cdot \frac{\vec R_u\times \vec R_v}{|\vec R_u\times\vec R_v|} |\vec R_u\times \vec R_v|dudv =\pm \iint_{(u,v)}\vec F\cdot \vec R_u\times \vec R_vdudv$$where the limits are for the region in the $u-v$ plane. Note that you never have to calculate $|\vec R_u\times\vec R_v|$. In your problem what he means by parameterizing the surface is writing it as $\vec R(x,y) = \langle x,y,9-x^2-y^2\rangle$. If you calculate $\vec R_x\times \vec R_y$ you will get $\langle 2x,2y,1\rangle$, which happens to have $z$ positive so agrees with your orientation, and agrees with your gradient. You have calculated $\nabla \times \vec F = \langle -4,6,-3\rangle$, which is the $\vec F$ to put in the formula above:$$\iint_S \langle -4,6,-3\rangle\cdot d\vec S = +\iint_{(x,y)}\langle -4,6,-3\rangle\cdot \langle 2x,2y,1\rangle dydx=\iint_{(x,y)}-8x+12y-3\ dydx$$where the $x-y$ limits are over the region in the $xy\$plane. That is where $z=0$ and gives the region enclosed by $x^2+y^2=9$. At this point, you might want to work the integral in polar coordinates.
Then, of course, you still have to work the other side of the Stokes Theorem equation and see you get the same answer.
10. May 6, 2012
### jerzey101
Thanks LCKurtz, that is similar to what we were doing in my class. I was getting confused by what sharks was doing.
11. May 6, 2012
### sharks
If you had continued from what my suggestion, you would have ended up with the same double integral:
$$\iint_{(x,y)}-8x+12y-3\ dydx$$
But it's indeed easier for you to understand if you can relate directly to what you're doing in class.
12. May 7, 2012
### jerzey101
Ok I'm starting to get it. Thank sharks!
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2018-06-25 06:33:10
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https://orbit.dtu.dk/en/publications/design-manufacturing-and-testing-of-a-2030-ghz-dual-band-circular
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Design, Manufacturing, and Testing of a 20/30-GHz Dual-Band Circularly Polarized Reflectarray Antenna
Thomas Gunst Smith, Ulrich Gothelf, Oleksiy S. Kim, Olav Breinbjerg
Research output: Contribution to journalJournal articleResearchpeer-review
Abstract
This letter documents the design, manufacturing, and testing of a single-layer dual-band circularly polarized reflectarray antenna for 19.7–20.2 and 29.5–30.0 GHz. The reflectarray is designed using the concentric dual split-loop element and the variable rotation technique that enables full 360$^{\circ}$ phase adjustment simultaneously in two separate frequency bands. The elements have been optimized to suppress cross-polar reflection. Thereafter, the element data is included in a design tool that computes the reflectarray layout and the associated radiation patterns. The reflectarray is composed of 80$\,\times\,$80 elements printed on a $40\times 40{\hbox{-cm}}^{2}$ Rogers 5880 substrate. The antenna has been manufactured and measured at the DTU-ESA Spherical Near-Field Antenna Test Facility. The peak gain is 35.8 and 40.0 dBi at 20.0 and 29.8 GHz, respectively, and the aperture illumination efficiency is in the range of 53%–63% over the two frequency bands.
Original language English IEEE Antennas and Wireless Propagation Letters 12 1480-1483 1536-1225 https://doi.org/10.1109/LAWP.2013.2288995 Published - 2013
Keywords
• Fields, Waves and Electromagnetics
• Circularly polarized
• Concentric dual split-loop
• Dual-band
• Ka-band
• Reflectarray
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2021-05-19 02:42:13
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